Question 1

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 2

A hiker walks 2 km east and then 1 km north. What is the magnitude of the resultant displacement?

Accepted Answer

$$\sqrt{5.00}\ \mathrm{km}$$

Question 3

Which of the following statements about displacement is correct?

Accepted Answer

Displacement is the straight-line vector from the starting to the ending position.

Question 4

If a vector $$\vec{A}$$ has a magnitude of 5 units and points along the positive x-axis, what are its components?

Accepted Answer

$$A_x = 5,\ A_y = 0$$

Question 5

Which equation correctly gives the x-component of a vector $$\vec{A} at an $$angle $$	heta$$ from the x-axis?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 6

A car travels 10 km north, then 10 km east. What is the total distance traveled and the magnitude of the displacement?

Accepted Answer

Distance: $$20\ \mathrm{km}$$, Displacement: $$10\sqrt{2}\ \mathrm{km}$$

Question 7

Which of the following is true about multiplying a vector by a negative scalar?

Accepted Answer

The magnitude changes and the direction reverses.

Question 8

If $$\vec{A}$$ and $$\vec{B}$$ are parallel vectors, what is the magnitude of their sum $$\vec{C}$$?

Accepted Answer

$$C = A + B$$

Question 9

A student walks 3 km west, then 4 km south. What is the magnitude of the resultant displacement?

Accepted Answer

$$5\ \mathrm{km}$$

Question 10

Which trigonometric function gives the ratio of the opposite side to the hypotenuse in a right triangle?

Accepted Answer

$$\sin 	heta$$

Question 11

What is the value of $$\pi$$ radians in degrees?

Accepted Answer

$$180^\circ$$

Question 12

A vector $$\vec{A}$$ has components $$A_x = 6$$ and $$A_y = 8. $$What is the magnitude $$|\vec{A}|$$?

Accepted Answer

$$10$$

Question 13

Which of the following is NOT a property of vector addition?

Accepted Answer

Multiplicative property

Question 14

If $$\vec{A}$$ and $$\vec{B}$$ are antiparallel, what is the magnitude of their sum $$\vec{C}$$?

Accepted Answer

$$C = |A - B|$$

Question 15

A vector $$\vec{A}$$ makes an angle $$	heta$$ with the x-axis. Which formula gives the y-component?

Accepted Answer

$$A_y = A \sin 	heta$$

Question 16

A person walks 5 km north, then 12 km east. What is the magnitude of the resultant displacement?

Accepted Answer

$$13\ \mathrm{km}$$

Question 17

Which of the following is a scalar quantity?

Accepted Answer

Distance

Question 18

If $$\vec{A} = 3\hat{i} + 4\hat{j}$$, what is the direction angle $$	heta$$ with respect to the x-axis?

Accepted Answer

$$	heta = \arctan(4/3)$$

Question 19

A vector $$\vec{A} is $$multiplied by a scalar $$k = 2. $$What happens to the vector?

Accepted Answer

Its magnitude doubles and direction remains the same.

Question 20

Which of the following best describes the result of adding two perpendicular vectors of equal magnitude $$A$$?

Accepted Answer

$$A\sqrt{2}$$

Vectors and Vector Addition: Foundations for Classical Mechanics

Study Guide - Practice Questions