Q: Given $$A_x = 6$$ and $$A_y = 8$$, what is the direction of the vector $$\vec{A}$$ with respect to the x-axis?

$$\theta = \tan$$^{-1}$$ \left( \frac{8}{6} \right)$$

Question 1

Which of the following is a scalar quantity?

Accepted Answer

Mass

Question 2

A vector is completely specified by:

Accepted Answer

A number, a unit, and a direction

Question 3

If a vector has a magnitude of 10 units and points 30° north of east, what are its x and y components?

Accepted Answer

$$A_x = 10 \cos 30^\circ$$, $$A_y = 10 \sin 30^\circ$$

Question 4

Two vectors are equal if and only if:

Accepted Answer

They have the same magnitude and direction

Question 5

If vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 4$$, what is its magnitude?

Accepted Answer

$$5$$

Question 6

If $$\vec{A} + \vec{B} = \vec{0}$$, what can you say about $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

They have the same magnitude and are in opposite directions

Question 7

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

Accepted Answer

Its magnitude is doubled and its direction is reversed

Question 8

Given $$A_x = 6$$ and $$A_y = 8$$, what is the direction of the vector $$\vec{A}$$ with respect to the x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$ \left( \frac{8}{6} ight)$$

Question 9

If each component of a vector is doubled, what happens to the angle of that vector?

Accepted Answer

It does not change

Question 10

A displacement vector has $$x$$ component $$-24.0 m $$and $$y$$ component $$-11.0 m. $$What is its magnitude?

Accepted Answer

$$\sqrt{(-24.0)^2$ + (-11.0)^2$}$$

Question 11

Which of the following best describes the result of adding two perpendicular vectors of equal magnitude?

Accepted Answer

A vector with magnitude $$A\sqrt{2} at 45$$° to each original vector

Question 12

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

Accepted Answer

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

Question 13

If $$\vec{A}$$ points due north and $$\vec{B}$$ points due west, both with the same magnitude, which of the following vectors points southwest?

Accepted Answer

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

Question 14

A vector $$\vec{A}$$ has a magnitude of 6.00 units and points due east. Vector $$\vec{B}$$ points due north. If $$\vec{A} + \vec{B}$$ points 60.0° north of east, what is the magnitude of $$\vec{B}$$?

Accepted Answer

$$6.00 	an 60.0^\circ$$

Question 15

Which of the following is NOT a property of a scalar quantity?

Accepted Answer

It has direction

Question 16

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

Accepted Answer

$$8\hat{j}$$

Question 17

A vector $$\vec{A} is $$resolved into components $$A_x$$ and $$A_y. If$$ $$A_x  0$$, in which quadrant does $$\vec{A}$$ lie?

Accepted Answer

Quadrant II

Question 18

If you travel 62.0 km in a direction 30.0° north of east, then 23.0 km in a direction 50.0° south of east, what is the x-component of your total displacement?

Accepted Answer

$$62.0 \cos 30.0^\circ + 23.0 \cos 50.0^\circ$$

Question 19

Which operation is equivalent to subtracting vector $$\vec{B}$$ from vector $$\vec{A}$$?

Accepted Answer

$$\vec{A} + (-\vec{B})$$

Chapter 1: Vectors – Models, Measurements & Vectors in Physics

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