$$\tan$$^{-1}$$\left(\frac{4}{3}\right)$$

Question 1

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 2

A car travels 100 meters east, then 100 meters north. What is the magnitude of its displacement?

Accepted Answer

$$141\ \mathrm{m}$$

Question 3

Given a vector $$\vec{A}$$ with magnitude $$A = 10$$ and direction $$	heta = 30^\circ$$ above the x-axis, what is the y-component $$A_y$$?

Accepted Answer

$$A_y = 10 \sin 30^\circ$$

Question 4

Which of the following best describes the magnitude of a vector?

Accepted Answer

It is always positive.

Question 5

A vector $$\vec{B}$$ has components $$B_x = -3$$ and $$B_y = 4. $$What is the magnitude of $$\vec{B}$$?

Accepted Answer

$$5$$

Question 6

Which of the following is NOT a vector quantity?

Accepted Answer

Power

Question 7

A vector $$\vec{C}$$ has a magnitude of $$8$$ and points at $$150^\circ ($$trig direction). What is the x-component $$C_x$$?

Accepted Answer

$$C_x = 8 \cos 150^\circ$$

Question 8

Which of the following statements is TRUE about vector components?

Accepted Answer

Vector components can be either positive or negative.

Question 9

A plane flies with a velocity of $$200\ \mathrm{km/h} at$$ $$30^\circ$$ north of east. What is the eastward (x) component of its velocity?

Accepted Answer

$$200 \cos 30^\circ$$

Question 10

If a vector $$\vec{D}$$ has components $$D_x = 0$$ and $$D_y = -5$$, what is its direction (trig angle)?

Accepted Answer

$$270^\circ$$

Question 11

Which of the following is a correct way to write a vector in unit-vector notation?

Accepted Answer

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

Question 12

A hiker walks $$3 km $$east and then $$4 km $$north. What is the direction of the displacement vector from the starting point (relative to east)?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{4}{3}ight)$$

Question 13

Which of the following is a scalar quantity?

Accepted Answer

Speed

Question 14

A vector has components $$A_x = 5$$ and $$A_y = 5. $$What is its direction (trig angle)?

Accepted Answer

$$45^\circ$$

Question 15

Which of the following best describes the difference between a scalar and a vector?

Accepted Answer

A vector has both magnitude and direction; a scalar has only magnitude.

Question 16

A vector $$\vec{E}$$ has a magnitude of $$12$$ and points at $$210^\circ. $$What is the y-component $$E_y$$?

Accepted Answer

$$E_y = 12 \sin 210^\circ$$

Question 17

Which of the following is true about the magnitude of a vector?

Accepted Answer

It is always positive, regardless of direction.

Question 18

A vector $$\vec{F}$$ has components $$F_x = -6$$ and $$F_y = -8. $$What is the magnitude of $$\vec{F}$$?

Accepted Answer

$$10$$

Question 19

Which of the following is a correct statement about vector translation?

Accepted Answer

A vector can be moved anywhere in space as long as its magnitude and direction remain unchanged.

Vectors, Scalars, and Vector Components: Study Guide

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