Exam 3: Vectors and Coordinate Systems

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In the figure, the magnitude of vector In the figure, the magnitude of vector   is 18.0 units, and the magnitude of vector   is 12.0 units. What vector   must be added to the vectors   and   so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.  is 18.0 units, and the magnitude of vector In the figure, the magnitude of vector   is 18.0 units, and the magnitude of vector   is 12.0 units. What vector   must be added to the vectors   and   so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.  is 12.0 units. What vector In the figure, the magnitude of vector   is 18.0 units, and the magnitude of vector   is 12.0 units. What vector   must be added to the vectors   and   so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.  must be added to the vectors In the figure, the magnitude of vector   is 18.0 units, and the magnitude of vector   is 12.0 units. What vector   must be added to the vectors   and   so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.  and In the figure, the magnitude of vector   is 18.0 units, and the magnitude of vector   is 12.0 units. What vector   must be added to the vectors   and   so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.  so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector In the figure, the magnitude of vector   is 18.0 units, and the magnitude of vector   is 12.0 units. What vector   must be added to the vectors   and   so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.  by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive. In the figure, the magnitude of vector   is 18.0 units, and the magnitude of vector   is 12.0 units. What vector   must be added to the vectors   and   so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.

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Vector Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? = -1.00 Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? + -2.00 Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? and vector Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? = 3.00 Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? + 4.00 Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? . What are the magnitude and direction of vector Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? = 3.00 Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? + 2.00 Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ? ?

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You walk You walk   to the north, then turn 60° to your right and walk another   How far are you from where you originally started? to the north, then turn 60° to your right and walk another You walk   to the north, then turn 60° to your right and walk another   How far are you from where you originally started? How far are you from where you originally started?

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A rabbit trying to escape a fox runs north for 8.0 m, darts northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit?

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If A > B, under what condition is | If A > B, under what condition is |   -   | = A - B? - If A > B, under what condition is |   -   | = A - B? | = A - B?

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Which of the following is an accurate statement?

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Vector Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? = 1.00 Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? + -2.00 Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? and vector Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? = 3.00 Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? + 4.00 Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? . What are the magnitude and direction of vector Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? = Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? + Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   =   +   ? ?

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The components of vector The components of vector   are   = + 3.90 and   = -4.00. What is the angle measured counterclockwise from the +x-axis to vector   ? are The components of vector   are   = + 3.90 and   = -4.00. What is the angle measured counterclockwise from the +x-axis to vector   ? = + 3.90 and The components of vector   are   = + 3.90 and   = -4.00. What is the angle measured counterclockwise from the +x-axis to vector   ? = -4.00. What is the angle measured counterclockwise from the +x-axis to vector The components of vector   are   = + 3.90 and   = -4.00. What is the angle measured counterclockwise from the +x-axis to vector   ? ?

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Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,   = 8.0 N and   = 7.0 N, where N is the standard unit of force, what is the component of the net force   <sub>net</sub> =   <sub>1 </sub>+   <sub>2 </sub>+   <sub>3</sub> parallel to the floor?  = 1.0 N, Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,   = 8.0 N and   = 7.0 N, where N is the standard unit of force, what is the component of the net force   <sub>net</sub> =   <sub>1 </sub>+   <sub>2 </sub>+   <sub>3</sub> parallel to the floor?  = 8.0 N and Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,   = 8.0 N and   = 7.0 N, where N is the standard unit of force, what is the component of the net force   <sub>net</sub> =   <sub>1 </sub>+   <sub>2 </sub>+   <sub>3</sub> parallel to the floor?  = 7.0 N, where N is the standard unit of force, what is the component of the net force Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,   = 8.0 N and   = 7.0 N, where N is the standard unit of force, what is the component of the net force   <sub>net</sub> =   <sub>1 </sub>+   <sub>2 </sub>+   <sub>3</sub> parallel to the floor?  net = Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,   = 8.0 N and   = 7.0 N, where N is the standard unit of force, what is the component of the net force   <sub>net</sub> =   <sub>1 </sub>+   <sub>2 </sub>+   <sub>3</sub> parallel to the floor?  1 + Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,   = 8.0 N and   = 7.0 N, where N is the standard unit of force, what is the component of the net force   <sub>net</sub> =   <sub>1 </sub>+   <sub>2 </sub>+   <sub>3</sub> parallel to the floor?  2 + Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,   = 8.0 N and   = 7.0 N, where N is the standard unit of force, what is the component of the net force   <sub>net</sub> =   <sub>1 </sub>+   <sub>2 </sub>+   <sub>3</sub> parallel to the floor?  3 parallel to the floor? Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,   = 8.0 N and   = 7.0 N, where N is the standard unit of force, what is the component of the net force   <sub>net</sub> =   <sub>1 </sub>+   <sub>2 </sub>+   <sub>3</sub> parallel to the floor?

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If If   -   = 0, then the vectors   and   have equal magnitudes and are directed in the opposite directions from each other. - If   -   = 0, then the vectors   and   have equal magnitudes and are directed in the opposite directions from each other. = 0, then the vectors If   -   = 0, then the vectors   and   have equal magnitudes and are directed in the opposite directions from each other. and If   -   = 0, then the vectors   and   have equal magnitudes and are directed in the opposite directions from each other. have equal magnitudes and are directed in the opposite directions from each other.

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A teacher sends her students on a treasure hunt. She gives the following instructions: 1. Walk 300 m north 2) Walk 400 m northwest 3) Walk 700 m east-southeast and the treasure is buried there. As all the other students walk off following the instructions, Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane need to walk?

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The components of vector The components of vector   are   = -3.5 and   = -9.7, and the components of vector   are   = -6 and   = +8.1. What is the angle (less than 180 degrees) between vectors   and   ? are The components of vector   are   = -3.5 and   = -9.7, and the components of vector   are   = -6 and   = +8.1. What is the angle (less than 180 degrees) between vectors   and   ? = -3.5 and The components of vector   are   = -3.5 and   = -9.7, and the components of vector   are   = -6 and   = +8.1. What is the angle (less than 180 degrees) between vectors   and   ? = -9.7, and the components of vector The components of vector   are   = -3.5 and   = -9.7, and the components of vector   are   = -6 and   = +8.1. What is the angle (less than 180 degrees) between vectors   and   ? are The components of vector   are   = -3.5 and   = -9.7, and the components of vector   are   = -6 and   = +8.1. What is the angle (less than 180 degrees) between vectors   and   ? = -6 and The components of vector   are   = -3.5 and   = -9.7, and the components of vector   are   = -6 and   = +8.1. What is the angle (less than 180 degrees) between vectors   and   ? = +8.1. What is the angle (less than 180 degrees) between vectors The components of vector   are   = -3.5 and   = -9.7, and the components of vector   are   = -6 and   = +8.1. What is the angle (less than 180 degrees) between vectors   and   ? and The components of vector   are   = -3.5 and   = -9.7, and the components of vector   are   = -6 and   = +8.1. What is the angle (less than 180 degrees) between vectors   and   ? ?

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The magnitude of a vector can never be less than the magnitude of one of its components.

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The components of vector The components of vector   are   = +2.2 and   = -6.9 , and the components of vector   are given are   = -6.1 and   = -2.2. What is the magnitude of the vector   -   ? are The components of vector   are   = +2.2 and   = -6.9 , and the components of vector   are given are   = -6.1 and   = -2.2. What is the magnitude of the vector   -   ? = +2.2 and The components of vector   are   = +2.2 and   = -6.9 , and the components of vector   are given are   = -6.1 and   = -2.2. What is the magnitude of the vector   -   ? = -6.9 , and the components of vector The components of vector   are   = +2.2 and   = -6.9 , and the components of vector   are given are   = -6.1 and   = -2.2. What is the magnitude of the vector   -   ? are given are The components of vector   are   = +2.2 and   = -6.9 , and the components of vector   are given are   = -6.1 and   = -2.2. What is the magnitude of the vector   -   ? = -6.1 and The components of vector   are   = +2.2 and   = -6.9 , and the components of vector   are given are   = -6.1 and   = -2.2. What is the magnitude of the vector   -   ? = -2.2. What is the magnitude of the vector The components of vector   are   = +2.2 and   = -6.9 , and the components of vector   are given are   = -6.1 and   = -2.2. What is the magnitude of the vector   -   ? - The components of vector   are   = +2.2 and   = -6.9 , and the components of vector   are given are   = -6.1 and   = -2.2. What is the magnitude of the vector   -   ? ?

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For the vectors shown in the figure, express vector For the vectors shown in the figure, express vector   in terms of vectors   and   .  in terms of vectors For the vectors shown in the figure, express vector   in terms of vectors   and   .  and For the vectors shown in the figure, express vector   in terms of vectors   and   .  . For the vectors shown in the figure, express vector   in terms of vectors   and   .

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Vectors Vectors   and   are shown in the figure. What is   ?  and Vectors   and   are shown in the figure. What is   ?  are shown in the figure. What is Vectors   and   are shown in the figure. What is   ?  ? Vectors   and   are shown in the figure. What is   ?

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If If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? = +4 If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? - 2 If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? - 3 If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? and If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? = -4 If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? -2 If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? - 3 If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? , which of the following numbers is closest to the magnitude of If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? - If   = +4   - 2   - 3   and   = -4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ? ?

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If the eastward component of vector If the eastward component of vector   is equal to the westward component of vector   and their northward components are equal. Which one of the following statements about these two vectors is correct? is equal to the westward component of vector If the eastward component of vector   is equal to the westward component of vector   and their northward components are equal. Which one of the following statements about these two vectors is correct? and their northward components are equal. Which one of the following statements about these two vectors is correct?

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Vectors Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  and Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  are shown in the figure. Vector Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  is given by Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  = Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  - Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  . The magnitude of vector Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  is 16.0 units, and the magnitude of vector Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  is 7.00 units. What is the magnitude of vector Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?  ? Vectors   and   are shown in the figure. Vector   is given by   =   -   . The magnitude of vector   is 16.0 units, and the magnitude of vector   is 7.00 units. What is the magnitude of vector   ?

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Under what condition is | Under what condition is |   -   | = A + B? - Under what condition is |   -   | = A + B? | = A + B?

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