Question 1

Given the vector $ \vec{A} $ in image 1 has a magnitude of 8.0 m and points directly downward along the negative y-axis, what are its x and y components?

Accepted Answer

$A_x = 0, \quad A_y = -8.0$

Question 2

For vector $ \vec{B} $ in image 1, which has a magnitude of 15.0 m and is oriented 30° above the positive x-axis, what is the correct expression for its x-component?

Accepted Answer

$B_x = 15.0 \cos 30^\circ$

Question 3

What is the y-component of vector $ \vec{C} $ in image 1, given its magnitude is 12.0 m and it is 25° below the negative x-axis?

Accepted Answer

$C_y = -12.0 \sin 25^\circ$

Question 4

If vectors $ \vec{A} $, $ \vec{B} $, and $ \vec{C} $ in image 2 are added head-to-tail, which vector equation correctly represents the resultant $ \vec{R} $?

Accepted Answer

$\vec{R} = \vec{A} + \vec{B} + \vec{C}$

Question 5

In image 3, what is the x-component of vector $ \vec{A} $ (100.0 N, 30° above the x-axis)?

Accepted Answer

$A_x = 100.0 \cos 30^\circ$

Question 6

Which of the following best describes the process for finding the magnitude of the resultant vector $ \vec{R} $ when adding three vectors $ \vec{A} $, $ \vec{B} $, and $ \vec{C} $ given in component form?

Accepted Answer

$|\vec{R}| = \sqrt{(A_x + B_x + C_x)^2 + (A_y + B_y + C_y)^2}$

Question 7

A force vector $ \vec{F} $ has components $F_x = 60.0$ N and $F_y = 80.0$ N. What is the magnitude of $ \vec{F} $?

Accepted Answer

$|\vec{F}| = \sqrt{60.0^2 + 80.0^2} = 100.0$ N

Question 8

If vector $ \vec{D} $ in image 1 has a magnitude of 10.0 m and is 53° above the negative x-axis, what is the correct expression for its x-component?

Accepted Answer

$D_x = -10.0 \cos 53^\circ$

Question 9

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

Accepted Answer

$V_y = V \sin 	heta$

Question 10

In image 3, if you want to find the net force acting at point O by adding vectors $ \vec{A} $, $ \vec{B} $, and $ \vec{C} $, what is the first step?

Accepted Answer

Resolve each vector into its x and y components.

Question 11

A vector $ \vec{P} $ has components $P_x = -20$ and $P_y = 20$. What is the direction of $ \vec{P} $ relative to the positive x-axis?

Accepted Answer

$135^\circ$

Question 12

Which of the following statements about vector addition is correct?

Accepted Answer

The resultant vector is independent of the order in which vectors are added.

Question 13

If a force vector $ \vec{F} $ is doubled in magnitude but its direction remains unchanged, what happens to its x and y components?

Accepted Answer

Both components are doubled.

Question 14

A vector $ \vec{Q} $ has a magnitude of 10 units and points at $60^\circ$ above the x-axis. What is its y-component?

Accepted Answer

$Q_y = 10 \sin 60^\circ$

Question 15

Which of the following is a correct method to subtract vector $ \vec{B} $ from vector $ \vec{A} $?

Accepted Answer

$\vec{A} - \vec{B}$

Question 16

If the resultant of two vectors is zero, what can you conclude about the vectors?

Accepted Answer

They are equal in magnitude and opposite in direction.

Vectors: Representation, Addition, and Components

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