$$x = 43.3\ \text{km},\ y = 25.0\ \text{km}$$

$$\theta = \tan$$^{-1}$$\left(\frac{3}{4}\right) = 36.9^\circ$$

Question 1

A car travels 50 km at an angle of $$30^\circ$$ north of east. What are the $$x$$ and $$y$$ components of the car's displacement?

Accepted Answer

$$x = 43.3\ 	ext{km},\ y = 25.0\ 	ext{km}$$

Question 2

Which of the following is a vector quantity?

Accepted Answer

Velocity

Question 3

Given a vector $$\vec{A} = 3\hat{i} - 4\hat{j}$$, what is its magnitude?

Accepted Answer

$$5$$

Question 4

If a vector $$\vec{B}$$ has a magnitude of $$10$$ and points at $$120^\circ$$ from the positive $$x-$$axis, what is its $$x-$$component?

Accepted Answer

$$-5$$

Question 5

A vector $$\vec{C} is $$multiplied by a scalar $$-2. $$What happens to the vector?

Accepted Answer

Its magnitude doubles and its direction reverses.

Question 6

Which of the following best describes a scalar quantity?

Accepted Answer

A quantity described by a single signed number.

Question 7

Given two vectors $$\vec{A} = 2\hat{i} + 1\hat{j}$$ and $$\vec{B} = -3\hat{i} + 2\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$-1\hat{i} + 3\hat{j}$$

Question 8

If $$\vec{D} = 4\hat{i} + 3\hat{j}$$, what is the direction angle $$	heta$$ with respect to the positive $$x-$$axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{3}{4}ight) = 36.9^\circ$$

Question 9

A point is located at $$(-4, 3) in $$Cartesian coordinates. What is its polar coordinate representation $$(r, 	heta)$$?

Accepted Answer

$$(5, 143^\circ)$$

Question 10

Which operation will result in a vector with the same direction but half the magnitude of $$\vec{E}$$?

Accepted Answer

$$0.5\vec{E}$$

Question 11

If $$\vec{F} = 5\hat{i} - 12\hat{j}$$, what is the magnitude of $$\vec{F}$$?

Accepted Answer

$$13$$

Question 12

A vector has components $$x = -3$$ and $$y = 4. In $$which quadrant does this vector lie?

Accepted Answer

Second quadrant

Question 13

Which of the following is the correct formula for the magnitude of a vector $$\vec{A} = a_x\hat{i} + a_y\hat{j}$$?

Accepted Answer

$$A = \sqrt{a_x^2$ + a_y^2$}$$

Question 14

A vector $$\vec{G}$$ has a magnitude of $$6$$ and points $$45^\circ$$ south of west. What are its $$x$$ and $$y$$ components?

Accepted Answer

$$x = -4.24,\ y = -4.24$$

Question 15

If $$\vec{A} = 2.0, \angle 30^\circ$$ and $$\vec{B} = 3.0, \angle 120^\circ$$, what is the magnitude of $$\vec{A} + \vec{B}$$?

Accepted Answer

$$2.24$$

Question 16

Which of the following statements about unit vectors is correct?

Accepted Answer

A unit vector has a magnitude of one and indicates direction.

Vectors and Coordinate Systems: Physics Study Guide

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