Question 1

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

Accepted Answer

A) 3.61 in a direction -56.3° counterclockwise from the positive x-axis 
B) 3.61 in a direction 56.3° counterclockwise from the positive x-axis 
C) 3.61 in a direction 33.7° counterclockwise from the positive x-axis 
D) 5.00 in a direction 56.3° counterclockwise from the positive x axis 
E) 6.72 in a direction 34.4° counterclockwise from the positive x-axis 
A) 3.61 in a direction -56.3° counterclockwise from the positive x-axis 
B) 3.61 in a direction 56.3° counterclockwise from the positive x-axis 
C) 3.61 in a direction 33.7° counterclockwise from the positive x-axis 
D) 5.00 in a direction 56.3° counterclockwise from the positive x axis 
E) 6.72 in a direction 34.4° counterclockwise from the positive x-axis C

Question 2

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

Accepted Answer

A) True 
 B)False  True

Question 3

Which of the following is an accurate statement?

Accepted Answer

A) The magnitude of a vector can be zero even though one of its components is not zero. 
B) It is possible to add a scalar quantity to a vector. 
C) Even though two vectors have unequal magnitudes,it is possible that their vector sum is zero. 
D) Rotating a vector about an axis passing through the tip of the vector does not change the vector. 
E) The magnitude of a vector is independent of the coordinate system used. 
A) The magnitude of a vector can be zero even though one of its components is not zero. 
B) It is possible to add a scalar quantity to a vector. 
C) Even though two vectors have unequal magnitudes,it is possible that their vector sum is zero. 
D) Rotating a vector about an axis passing through the tip of the vector does not change the vector. 
E) The magnitude of a vector is independent of the coordinate system used. E

Question 4

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?

Accepted Answer

A) 8.8 m 
B) 8.1 m 
C) 66 m 
D) 10 m 
A) 8.8 m 
B) 8.1 m 
C) 66 m 
D) 10 m

Question 5

You walk 53 m to the north,then turn 60° to your right and walk another   Determine the direction of your displacement vector.Express your answer as an angle relative to east.

Accepted Answer

A) 63° N of E 
B) 50° N of E 
C) 57° N of E 
D) 69° N of E 
A) 63° N of E 
B) 50° N of E 
C) 57° N of E 
D) 69° N of E

Question 6

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

Accepted Answer

A) 8 
B) 7 
C) 9 
D) 10 
E) 11 
A) 8 
B) 7 
C) 9 
D) 10 
E) 11

Question 7

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

Accepted Answer

A) The statement is never true. 
B) Vectors   and   are in opposite directions. 
C) Vectors   and   are in the same direction. 
D) Vectors   and   re in perpendicular directions. 
E) The statement is always true. 
A) The statement is never true. 
B) Vectors   and   are in opposite directions. 
C) Vectors   and   are in the same direction. 
D) Vectors   and   re in perpendicular directions. 
E) The statement is always true.

Question 8

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   ?

Accepted Answer

A) 124° 
B) 56° 
C) 17° 
D) 163° 
E) 106° 
A) 124° 
B) 56° 
C) 17° 
D) 163° 
E) 106°

Question 9

Vector   has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis.What are the x and y components of vector   .

Accepted Answer

A) Ax = 3.83 and Ay = 3.21 
B) Ax = 3.83 and Ay = -3.21 
C) Ax = -3.21 and Ay = -3.83 
D) Ax = -3.21 and Ay = 3.83 
E) Ax = 4.29 and Ay = 2.16 
A) Ax = 3.83 and Ay = 3.21 
B) Ax = 3.83 and Ay = -3.21 
C) Ax = -3.21 and Ay = -3.83 
D) Ax = -3.21 and Ay = 3.83 
E) Ax = 4.29 and Ay = 2.16

Question 10

If the magnitude of vector   is less than the magnitude of vector   ,then the x component of   is less than the x component of   .

Accepted Answer

A) True 
 B)False

Question 11

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

Accepted Answer

A) The magnitude of vector   is zero. 
B) Vectors   and   are in opposite directions. 
C) Vectors   and   are in the same direction. 
D) Vectors   and   are in perpendicular directions. 
E) The statement is never true. 
A) The magnitude of vector   is zero. 
B) Vectors   and   are in opposite directions. 
C) Vectors   and   are in the same direction. 
D) Vectors   and   are in perpendicular directions. 
E) The statement is never true.

Question 12

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

Accepted Answer

The answer of For the vectors shown in the figure,express...

Question 13

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

Accepted Answer

A) 7.21 in a direction 33.7° counterclockwise from the positive x axis 
B) 6.00 in a direction 63.4° counterclockwise from the positive x axis 
C) 4.47 in a direction 6.34° counterclockwise from the positive x axis 
D) 4.47 in a direction 26.6° counterclockwise from the positive x axis 
E) 7.21 in a direction 56.3° counterclockwise from the positive x axis 
A) 7.21 in a direction 33.7° counterclockwise from the positive x axis 
B) 6.00 in a direction 63.4° counterclockwise from the positive x axis 
C) 4.47 in a direction 6.34° counterclockwise from the positive x axis 
D) 4.47 in a direction 26.6° counterclockwise from the positive x axis 
E) 7.21 in a direction 56.3° counterclockwise from the positive x axis

Question 14

Vectors   and   are shown in the figure.What is   ?

Accepted Answer

A) 31.8 
B) -32.0   - 2.00   
C) 1028 
D) 34.0 
E) -2.00   - 32.0   
A) 31.8 
B) -32.0   - 2.00   
C) 1028 
D) 34.0 
E) -2.00   - 32.0

Question 15

What is the magnitude of   +   +   ,where   = 1.00   + 4.00   - 1.00   ,   = 3.00   - 1.00   - 4.00   and   = -1.00   + 1.00   ?

Accepted Answer

A) 7.07 
B) 2.00 
C) 10.76 
D) 6.78 
E) 8.12 
A) 7.07 
B) 2.00 
C) 10.76 
D) 6.78 
E) 8.12

Question 16

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?

Accepted Answer

A) Vector   is parallel to vector   . 
B) Vectors   and   point in opposite directions. 
C) Vector   is perpendicular to vector   . 
D) The magnitude of vector   is equal to the magnitude of vector   . 
E) The magnitude of vector   is twice the magnitude of vector   . 
A) Vector   is parallel to vector   . 
B) Vectors   and   point in opposite directions. 
C) Vector   is perpendicular to vector   . 
D) The magnitude of vector   is equal to the magnitude of vector   . 
E) The magnitude of vector   is twice the magnitude of vector   .

Question 17

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

Accepted Answer

A) 314° 
B) 134° 
C) 224° 
D) 136° 
E) 46.0° 
A) 314° 
B) 134° 
C) 224° 
D) 136° 
E) 46.0°

Question 18

Vector   has a magnitude of 75.0 cm and points at 30° above the positive x-axis.Vector   has a magnitude of 25.0 cm and points along the negative x-axis.Vector   has a magnitude of 40.0 cm and points at 45° below the negative x-axis.
(a)Determine the x and y components of Vector   .
(b)Determine the x and y components of Vector   .
(c)Determine the x and y components of Vector   .
(d)Determine x and y components of the sum of these three vectors.
(e)Determine the magnitude and direction of the sum of these three vectors.

Accepted Answer

(a) @#IMG-DLM& = 65 cm, @#IMG-DLM& = 38 cm
(b) @#IMG-DLM& =

Question 19

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   net =   1 +   2 +   3 parallel to the floor?

Accepted Answer

A) 2.5 N 
B) 5.1 N 
C) 6.0 N 
D) 7.8 N 
A) 2.5 N 
B) 5.1 N 
C) 6.0 N 
D) 7.8 N

Question 20

If all the components of a vector are equal to 1,then that vector is a unit vector.

Accepted Answer

A) True 
 B)False

Exam 3: Vectors and Coordinate Systems

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

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

Which of the following is an accurate statement?

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?

You walk 53 m to the north,then turn 60° to your right and walk another Determine the direction of your displacement vector.Express your answer as an angle relative to east.

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

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

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 ?

Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis.What are the x and y components of vector .

If the magnitude of vector is less than the magnitude of vector ,then the x component of is less than the x component of .

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

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

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

Vectors and are shown in the figure.What is ?

What is the magnitude of + + ,where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ?

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?

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

If all the components of a vector are equal to 1,then that vector is a unit vector.

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