Q: Which equation correctly expresses the scalar (dot) product of two vectors $\vec{A}$ and $\vec{B}$ in terms of their magnitudes and the angle $\theta$ between them?

$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos \theta$

Q: Which of the following is dimensionally consistent?

$\text{velocity} + \text{velocity}$

Q: Which of the following is the correct formula for the magnitude of the cross product $|\vec{A} \times \vec{B}|$?

$|\vec{A}| |\vec{B}| \sin \theta$

Question 1

Which of the following is NOT a fundamental quantity in the International System (SI) of units?

Accepted Answer

Temperature

Question 2

A student measures the length of a table as 2.345 m and its width as 1.2 m. What is the correct number of significant figures in the calculated area?

Accepted Answer

2

Question 3

Which equation correctly expresses the scalar (dot) product of two vectors $\vec{A}$ and $\vec{B}$ in terms of their magnitudes and the angle $	heta$ between them?

Accepted Answer

$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos 	heta$

Question 4

A car travels 3.0 km east and then 4.0 km north. What is the magnitude of its displacement from the starting point?

Accepted Answer

$5.0$ km

Question 5

Which of the following best describes a vector quantity?

Accepted Answer

It has both magnitude and direction.

Question 6

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

Accepted Answer

$10$

Question 7

Which prefix represents $10^{-9}$ in SI units?

Accepted Answer

nano-

Question 8

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

Accepted Answer

$10$

Question 9

Which of the following statements about the cross product $\vec{A} 	imes \vec{B}$ is TRUE?

Accepted Answer

Its direction is given by the right-hand rule.

Question 10

A train mishap occurs due to a small percent error in the measurement of time. Which concept does this scenario best illustrate?

Accepted Answer

The significance of uncertainty and significant figures.

Question 11

Which of the following is dimensionally consistent?

Accepted Answer

$	ext{velocity} + 	ext{velocity}$

Question 12

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

Accepted Answer

$|A - B|$

Question 13

Which of the following is the correct way to convert 3 minutes to seconds?

Accepted Answer

$3 	imes 60 = 180$ 	ext{ s}$

Question 14

Which of the following is a correct expression for a vector $\vec{A}$ in terms of its components and unit vectors?

Accepted Answer

$\vec{A} = A_x \hat{i} + A_y \hat{j}$

Question 15

A vector $\vec{B}$ has a magnitude of $5$ and points $60^\circ$ north of east. What are its $x$ and $y$ components?

Accepted Answer

$B_x = 2.5, B_y = 4.3$

Question 16

Which of the following is TRUE about unit vectors?

Accepted Answer

They have magnitude 1 and no units.

Question 17

If $\vec{A} = 3\hat{i} - 4\hat{j}$, what is the direction angle $	heta$ of $\vec{A}$ measured counterclockwise from the $+x$ axis?

Accepted Answer

$-53.1^\circ$ or $306.9^\circ$

Question 18

Which of the following is the correct formula for the magnitude of the cross product $|\vec{A} 	imes \vec{B}|$?

Accepted Answer

$|\vec{A}| |\vec{B}| \sin 	heta$

Question 19

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

Accepted Answer

Magnitude doubles, direction reverses.

Question 20

Which of the following is a correct statement about adding vectors graphically?

Accepted Answer

The head-to-tail method can be used to add any number of vectors.

Chapter 01

Study Guide - Practice Questions

Study Guide - Flashcards