Q: Which equation is used to find the direction angle $$\theta of a $$vector $$\vec{R}$$ with components $$R_x$$ and $$R_y$$?

$$\theta = \tan$$^{-1}$$ \left( \frac{R_y}{R_x} \right)$$

Question 1

Which of the following is a vector quantity?

Accepted Answer

Velocity

Question 2

A vector is represented by an arrow. What does the length of the arrow indicate?

Accepted Answer

The magnitude of the vector

Question 3

Which of the following correctly expresses the relation between vectors $$\vec{A}$$, $$\vec{B}$$, and $$\vec{C}$$ shown in a closed triangle?

Accepted Answer

$$\vec{A} + \vec{B} + \vec{C} = 0$$

Question 4

If a vector $$\vec{A}$$ has a magnitude of 36 m and a direction angle of $$60^\circ$$ with the $$+x-$$axis, what is the magnitude of vector $$\vec{B} = -\vec{A}/3$$?

Accepted Answer

12 m

Question 5

Which of the following is NOT a fundamental SI unit?

Accepted Answer

Newton

Question 6

A hiker walks 2.50 km at $$45.0^\circ$$ southeast from her car, then 4.00 km at $$60.0^\circ$$ north of east. What is the first step to find her total displacement?

Accepted Answer

Draw and find the x and y components of the first vector

Question 7

Which statement about multiplying a vector by a negative scalar is correct?

Accepted Answer

It reverses the direction of the vector

Question 8

Express the vector $$\vec{D}$$ with components $$D_x = 4$$, $$D_y = -2 in $$unit vector notation.

Accepted Answer

$$4\vec{i} - 2\vec{j}$$

Question 9

What is the magnitude of the velocity vector $$\vec{v} = (-4\vec{i} + 3\vec{j}) \frac{m}{s}$$?

Accepted Answer

$$5 \frac{m}{s}$$

Question 10

Which of the following is a scalar quantity?

Accepted Answer

Time

Question 11

In a Cartesian coordinate system, which unit vector points in the $$+y$$ direction?

Accepted Answer

$$\vec{j}$$

Question 12

If $$\vec{A}$$ has components $$A_x$$ and $$A_y$$, what is the formula for its magnitude?

Accepted Answer

$$A = \sqrt{A_x^2$ + A_y^2$}$$

Question 13

A vector $$\vec{A}$$ makes an angle $$	heta$$ with the $$x-$$axis. What is the $$y-$$component of $$\vec{A}$$?

Accepted Answer

$$A_y = A \sin 	heta$$

Question 14

Which of the following best describes equilibrium in mechanics?

Accepted Answer

Objects at rest or moving at constant velocity

Question 15

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

Accepted Answer

$$0\vec{i} + 6\vec{j}$$

Question 16

Which of the following is true about vector components?

Accepted Answer

They can be positive or negative

Question 17

A flying car travels 2.5 miles east by southeast from PHX to ASU. Which vector notation best describes this displacement using unit vectors $$\hat{e} ($$east) and $$\hat{n} ($$north)?

Accepted Answer

$$1.77 \hat{e} + 1.77 \hat{n}$$

Question 18

Which equation is used to find the direction angle $$	heta of a $$vector $$\vec{R}$$ with components $$R_x$$ and $$R_y$$?

Accepted Answer

$$	heta = 	an$$^{-1}$$ \left( \frac{R_y}{R_x} ight)$$

Question 19

Which of the following is a correct statement about unit vectors?

Accepted Answer

Unit vectors have magnitude 1 and no units

Fundamental Quantities, Units, and Vectors in Mechanics

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