Question 1

Which of the following physical quantities is a vector?

Accepted Answer

Velocity

Question 2

A box is pushed with two perpendicular forces: 12 N to the right and an unknown force upward. If the total force magnitude is 13 N, what is the magnitude of the upward force?

Accepted Answer

$$\sqrt{13^2$ - 12^2$} = 5\ \mathrm{N}$$

Question 3

When combining two perpendicular displacement vectors of 3 m east and 4 m north, what is the magnitude of the resultant displacement?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5\ \mathrm{m}$$

Question 4

A delivery truck travels 8 miles in the x-direction, 5 miles in the y-direction, and 4 miles again in the x-direction. What is the magnitude of its final displacement from the origin?

Accepted Answer

$$\sqrt{(8+4)^2$ + 5^2$} = \sqrt{144 + 25} = \sqrt{169} = 13\ \mathrm{miles}$$

Question 5

Which statement about vector addition is correct?

Accepted Answer

The resultant vector is always the shortest path from the start of the first vector to the end of the last.

Question 6

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

Accepted Answer

$$\sqrt{(2 + (-1))^2$ + (3 + 4)^2$} = \sqrt{1^2$ + 7^2$} = \sqrt{50} \approx 7.07$$

Question 7

A vector $$\vec{A}$$ has a y-component of 12 and makes an angle of $$67.4^\circ$$ with the positive x-axis. What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$\frac{12}{\sin(67.4^\circ)} \approx 13.0$$

Question 8

If a vector $$\vec{F} is 8 $$units long and directed $$30.5^\circ$$ below the positive x-axis, what is its y-component $$F_y$$?

Accepted Answer

$$8 \sin(-30.5^\circ) \approx -4.06$$

Question 9

A small helicopter travels 225 m across a city in a direction $$53.1^\circ$$ south of east. What is the x-component of its trip?

Accepted Answer

$$225 \cos(53.1^\circ) \approx 135.0\ \mathrm{m}$$

Question 10

Which of the following is the correct unit vector notation for $$\vec{A} = 4\hat{i} + 2\hat{j}$$ and $$\vec{B} = -1\hat{i} + 2\hat{j}$$?

Accepted Answer

$$\vec{A} + \vec{B} = 3\hat{i} + 4\hat{j}$$

Question 11

Given $$\vec{A} = 6\hat{i} - 3\hat{j} - 4\hat{k}$$ and $$\vec{B} = (0.6\hat{i} + 2\hat{j} - 5\hat{k})$$, what is the dot product $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$(6)(0.6) + (-3)(2) + (-4)(-5) = 3.6 - 6 + 20 = 17.6$$

Question 12

If $$\vec{A} = 2\hat{i} - 3\hat{j}$$ and $$\vec{B} = 2.1\hat{i} + 4.8\hat{j}$$, what is the angle $$	heta$$ between $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$	heta = \cos$$^{-1}$$\left(\frac{\vec{A} \cdot \vec{B}}{|\vec{A}||\vec{B}|}ight)$$

Question 13

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

Accepted Answer

The cross product produces a vector perpendicular to both $$\vec{A}$$ and $$\vec{B}.$$

Question 14

Two vectors $$\vec{A}$$ and $$\vec{B}$$ have a scalar product of $$-6$$ and a vector product magnitude of $$12. $$What is the angle between these two vectors?

Accepted Answer

$$	heta = \arccos\left(\frac{-6}{|\vec{A}||\vec{B}|}ight)$$ and $$\sin	heta = \frac{12}{|\vec{A}||\vec{B}|}$$, so $$	heta = 117^\circ$$

Question 15

Which formula correctly expresses the cross product of $$\vec{A} = a_1$\hat{i} + a_2$\hat{j} + a_3$\hat{k}$$ and $$\vec{B} = b_1$\hat{i} + b_2$\hat{j} + b_3$\hat{k} in $$component form?

Accepted Answer

$$\vec{A} 	imes \vec{B} = (a_2b_3 - a_3b_2)\hat{i} + (a_3b_1 - a_1b_3)\hat{j} + (a_1b_2 - a_2b_1)\hat{k}$$

Question 16

A vector $$\vec{C} is $$defined as $$\vec{C} = 2\hat{i} + 3\hat{j} + 6\hat{k}. $$What is the unit vector in the direction of $$\vec{C}$$?

Accepted Answer

$$\frac{2\hat{i} + 3\hat{j} + 6\hat{k}}{\sqrt{2^2$ + 3^2$ + 6^2$}}$$

Question 17

A vector $$\vec{A}$$ has components $$A_x = -77 cm $$and $$A_y = 36 cm. $$What is the absolute angle $$	heta of $$the vector from the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{36}{-77}ight) \approx -25.0^\circ (or$$ $$155^\circ$$ from positive x-axis)

Vectors: Comprehensive Study Notes for College Physics

Study Guide - Practice Questions

Study Guide - Flashcards