Question 1

Which of the following quantities is a vector?

Accepted Answer

Velocity

Question 2

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 3

Which of the following statements about unit vectors is correct?

Accepted Answer

Unit vectors have a magnitude of one and point in a specific direction.

Question 4

Given two vectors $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = -\hat{i} + 4\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$\hat{i} + 7\hat{j}$$

Question 5

If $$\vec{A}$$ and $$\vec{B}$$ are equal vectors, which of the following must be true?

Accepted Answer

They must have the same magnitude and direction.

Question 6

A pilot wants to fly directly north, but there is a wind blowing to the east. Which vector addition method best describes how the pilot should determine the required heading?

Accepted Answer

Tip-to-tail method

Question 7

Which of the following is the correct formula for the dot product of two vectors $$\vec{a}$$ and $$\vec{b}$$?

Accepted Answer

$$\vec{a} \cdot \vec{b} = ab \cos(\phi)$$

Question 8

What is the result of the cross product $$\hat{i} 	imes \hat{j}$$?

Accepted Answer

$$\hat{k}$$

Question 9

A force vector $$\vec{F} = 10\hat{i} + 5\hat{j} N $$acts on an object. What is the component of this force in the direction of the $$x-$$axis?

Accepted Answer

$$10 N$$

Question 10

Which of the following statements about the cross product is true?

Accepted Answer

The cross product is not commutative.

Question 11

If $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and $$\vec{B} = 2\hat{i} - \hat{j}$$, what is the dot product $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$10$$

Question 12

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

Accepted Answer

$$v_y = v \sin(	heta)$$

Question 13

Which of the following is a correct property of vector addition?

Accepted Answer

Vector addition is commutative: $$\vec{A} + \vec{B} = \vec{B} + \vec{A}$$

Question 14

A vector $$\vec{A} is $$multiplied by a scalar $$-2. $$What happens to the direction and magnitude of the resulting vector?

Accepted Answer

The magnitude doubles and the direction reverses.

Question 15

Given $$\vec{A} = 2\hat{i} + 3\hat{j} + 4\hat{k}$$ and $$\vec{B} = \hat{i} - 2\hat{j} + 2\hat{k}$$, what is the $$\hat{j}$$ component of $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

$$0$$

Question 16

Which of the following best describes the geometric meaning of the cross product $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

It gives a vector perpendicular to the plane formed by $$\vec{A}$$ and $$\vec{B}.$$

Question 17

A displacement vector has a magnitude of $$10 m $$and makes an angle of $$30^\circ$$ with the $$x-$$axis. What is its $$x-$$component?

Accepted Answer

$$10 \cos(30^\circ) = 8.66 m$$

Question 18

Which of the following is NOT a scalar quantity?

Accepted Answer

Momentum

Question 19

If $$\vec{A} = a_x \hat{i} + a_y \hat{j}$$ and $$\vec{B} = b_x \hat{i} + b_y \hat{j}$$, what is the formula for their cross product in the $$z-$$direction?

Accepted Answer

$$(a_x b_y - a_y b_x) \hat{k}$$

Vectors and Vector Operations (Ch. 3) - Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards