$$\theta = \arctan\left(\frac{-8}{6}\right)$$

$$\vec{A} = A \cos \theta \hat{i} + A \sin \theta \hat{j}$$

Question 1

Which of the following is NOT a scalar quantity?

Accepted Answer

Velocity

Question 2

Which of the following is the correct three-part definition of a vector?

Accepted Answer

A quantity with magnitude, direction, and units

Question 3

Which of the following is an example of a vector quantity?

Accepted Answer

Displacement

Question 4

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

Accepted Answer

$$5$$

Question 5

If a vector $$\vec{B} is $$multiplied by a scalar $$-2$$, what happens to its magnitude and direction?

Accepted Answer

The magnitude doubles and the direction reverses

Question 6

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

Accepted Answer

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

Question 7

Which of the following best describes a unit vector?

Accepted Answer

A vector with magnitude 1 in a specified direction

Question 8

A vector $$\vec{C}$$ has a magnitude of $$10$$ and makes an angle of $$30^\circ$$ with the x-axis. What is the x-component of $$\vec{C}$$?

Accepted Answer

$$10 \cos 30^\circ$$

Question 9

Which of the following is a correct way to express a vector in terms of its components?

Accepted Answer

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

Question 10

Given a vector $$\vec{D} = 6\hat{i} - 8\hat{j}$$, what is the angle $$	heta it $$makes with the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{-8}{6}ight)$$

Question 11

A car travels 100 km east and then 75 km north. What is the magnitude of its displacement?

Accepted Answer

$$\sqrt{100^2$ + 75^2$}$$

Question 12

If $$\vec{E} = 4\hat{i} + 3\hat{j}$$, what is the unit vector in the direction of $$\vec{E}$$?

Accepted Answer

$$\frac{4\hat{i} + 3\hat{j}}{5}$$

Question 13

Which of the following is a correct statement about the subtraction of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} - \vec{B} is $$equivalent to $$\vec{A} + (-\vec{B})$$

Question 14

A vector $$\vec{F} in 3D $$has components $$F_x = 2$$, $$F_y = -2$$, $$F_z = 1. $$What is the magnitude of $$\vec{F}$$?

Accepted Answer

$$\sqrt{2^2$ + (-2)^2$ + 1^2$}$$

Question 15

If a vector $$\vec{G} is $$multiplied by a scalar $$\frac{1}{2}$$, what happens to its magnitude?

Accepted Answer

It is halved

Question 16

Given $$\vec{H} = 5\hat{i} + 12\hat{j}$$, what is the angle its projection in the x-y plane makes with the x-axis?

Accepted Answer

$$\arctan\left(\frac{12}{5}\right)$$

Question 17

Which of the following is a correct statement about expressing a vector in terms of its magnitude and direction?

Accepted Answer

$$\vec{A} = A \cos 	heta \hat{i} + A \sin 	heta \hat{j}$$

Question 18

A pilot flies 200 km north, then 150 km east. What is the magnitude of the resultant displacement?

Accepted Answer

$$\sqrt{200^2$ + 150^2$}$$

Question 19

Which of the following is NOT a correct example of a scalar quantity?

Accepted Answer

Acceleration

Question 20

Given $$\vec{J} = 7\hat{i} - 24\hat{j}$$, what is the magnitude of $$\vec{J}$$?

Accepted Answer

$$25$$

Scalars and Vectors: Definitions, Properties, and Operations

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