Exam 2: Motion Along a Straight Line

Scalar (dot) product: The angle between vector = 2.00 + 3.00 and vector is The scalar product of vectors and is 3.00. If the x component of vector is positive, what is vector .

Components: 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 .

Vector (cross) product: If and are nonzero vectors for which ∙ = 0, it must follow that

Addition and subtraction: 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 ?

Addition and subtraction: 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 angle of vector , measured counterclockwise from the +x-axis?

Vector (cross) product: If = - 4 - 2 - 3 , what is × ?

Vector (cross) product: For the vectors shown in the figure, find the magnitude and direction of × , assuming that the quantities shown are accurate to two significant figures.

Vector (cross) product: If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors, what is the angle between the two vectors?

Scalar (dot) product: What is the angle between the vector = + 3 - 2 - 3 and the +y-axis?

Vector (cross) product: What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?

Scalar (dot) product: The scalar product of vector = 3.00 + 2.00 and vector is 10.0. Which of the following vectors could be vector ?

Components: 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 ?

Components: 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?

Components: Vector has a magnitude of 5.5 cm and points along the x-axis. Vector has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector . (c) Determine x and y components of the sum of these two vectors. (d) Determine the magnitude and direction of the sum of these two vectors.

Components: A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

Scalar (dot) product: If = 3 - + 4 and = x + - 5 , find x so will be perpendicular to .

Components: 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?

Scalar (dot) product: A rectangular box is positioned with its vertices at the following points: A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3) B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3) If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to:

Vector (cross) product: For the vectors shown in the figure, find the magnitude and direction of the vector product × that the quantities shown are accurate to two significant figures.

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