Question 1

Which of the following physical quantities is a vector?

Accepted Answer

Force

Question 2

A vector is completely specified by:

Accepted Answer

A magnitude and a direction

Question 3

If vector $\vec{A}$ has a magnitude of 5 units and points east, and vector $\vec{B}$ has a magnitude of 5 units and points north, what is the magnitude of the resultant vector $\vec{A} + \vec{B}$?

Accepted Answer

$\sqrt{5^2 + 5^2} = 7.07$

Question 4

Which statement is true about the sum of two vectors $\vec{A}$ and $\vec{B}$?

Accepted Answer

The magnitude and direction of $\vec{A} + \vec{B}$ depend on the angle between $\vec{A}$ and $\vec{B}$

Question 5

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

Accepted Answer

They have the same magnitude but opposite directions

Question 6

A vector $\vec{A}$ has components $A_x = 3$ and $A_y = 4$. What is the magnitude of $\vec{A}$?

Accepted Answer

$5$

Question 7

If a vector $\vec{A}$ is multiplied by a scalar $-2$, what happens to its magnitude and direction?

Accepted Answer

Magnitude is doubled, direction is reversed

Question 8

Given a displacement vector with $x$ component $-24.0$ m and $y$ component $-11.0$ m, what is its magnitude?

Accepted Answer

$\sqrt{(-24.0)^2 + (-11.0)^2} = 26.3$ m

Question 9

If the $x$ component of a vector is doubled, what happens to the angle the vector makes with the $x$-axis?

Accepted Answer

It decreases, but by less than half

Question 10

A runner travels 62.0 km in a direction $30.0^	ext{o}$ north of east, then turns and travels 23.0 km in a direction $50.0^	ext{o}$ south of east. What is the total eastward ($x$) component of the runner's displacement?

Accepted Answer

$62.0 \cos 30.0^	ext{o} + 23.0 \cos 50.0^	ext{o}$

Question 11

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

Accepted Answer

They require a direction for complete specification

Question 12

If vector $\vec{A}$ points due north and vector $\vec{B}$ points due west, both with equal magnitude, which direction does the vector $\vec{A} + (-\vec{B})$ point?

Accepted Answer

Northeast

Question 13

A vector $\vec{A}$ has components $A_x = -8$ and $A_y = 6$. What is the direction of $\vec{A}$ with respect to the positive $x$-axis?

Accepted Answer

$	an^{-1}(6/(-8))$

Question 14

Which of the following best describes the graphical representation of the negative of a vector $\vec{A}$?

Accepted Answer

It has the same magnitude but the opposite direction to $\vec{A}$

Question 15

If $\vec{C} = \vec{A} + \vec{B}$ and $\vec{A}$ and $\vec{B}$ are perpendicular, what is $|\vec{C}|$?

Accepted Answer

$\sqrt{|\vec{A}|^2 + |\vec{B}|^2}$

Question 16

A vector $\vec{A}$ has a magnitude of 6.00 units and points due east. Vector $\vec{B}$ is added to $\vec{A}$ such that $\vec{A} + \vec{B}$ points $60.0^	ext{o}$ north of east. What is the magnitude of $\vec{B}$?

Accepted Answer

$6.00 	an 60.0^	ext{o}$

Question 17

Which of the following is the correct formula for the $y$-component of a vector $\vec{A}$ with magnitude $A$ and angle $	heta$ with respect to the positive $x$-axis?

Accepted Answer

$A \sin 	heta$

Question 18

If you travel from your apartment to the corner of 1st Avenue and Park Street, then to the coffee house, what is your net displacement?

Accepted Answer

The straight-line vector from your apartment to the coffee house

Question 19

When resolving a vector into components, which trigonometric function is used to find the $x$-component if the angle is measured from the positive $x$-axis?

Accepted Answer

$\cos 	heta$

CH. 1 vectors

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