Question 1

If $\vec{A} + \vec{B} = 0$, which of the following must be true about vectors $\vec{A}$ and $\vec{B}$?

Accepted Answer

They have equal magnitudes and are in opposite directions.

Question 2

Given $|\vec{A}| > |\vec{B}|$, under what condition is $|\vec{A} - \vec{B}| = |\vec{A}| - |\vec{B}|$?

Accepted Answer

When $\vec{A}$ and $\vec{B}$ are in the same direction.

Question 3

Which of the following statements about vector components is correct?

Accepted Answer

The magnitude of a vector can never be less than the magnitude of one of its components.

Question 4

A helicopter is flying horizontally at $444\ \mathrm{m/s}$ over a hill that slopes upward at a $26^\circ$ grade. What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

Accepted Answer

$400\ \mathrm{m/s}$

Question 5

If $\vec{A} = 3.00\hat{i} + 4.00\hat{j}$ and $\vec{B} = 4.00\hat{i} - 3.00\hat{j}$, what is $\vec{A} + \vec{B}$?

Accepted Answer

$7.00\hat{i} + 1.00\hat{j}$

Question 6

You walk $55\ \mathrm{m}$ north, then turn $60^\circ$ to your right and walk another $45\ \mathrm{m}$. How far are you from your starting point?

Accepted Answer

$87\ \mathrm{m}$

Question 7

Given $\vec{A}$ has components $A_x = -3.21$ and $A_y = 3.83$, what is the magnitude of $\vec{A}$?

Accepted Answer

$5.00$

Question 8

If $\vec{A} = 2.2\hat{i} - 6.9\hat{j}$ and $\vec{B} = -6.1\hat{i} - 2.2\hat{j}$, what is the magnitude of $\vec{A} - \vec{B}$?

Accepted Answer

$9.1$

Question 9

Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes and their northward components are equal. Which statement is correct?

Accepted Answer

The magnitude of vector $\vec{A}$ is equal to the magnitude of vector $\vec{B}$.

Question 10

If all the components of a vector are equal to 1, then that vector is a unit vector. Is this statement true or false?

Accepted Answer

False

Question 11

Given $\vec{A} = 1.00\hat{i} + 2.00\hat{j}$ and $\vec{B} = 3.00\hat{i} + 4.00\hat{j}$, what is the magnitude and direction of $\vec{C} = \vec{A} - \vec{B}$?

Accepted Answer

$2.83$ in a direction $243.4^\circ$ counterclockwise from the positive x-axis

Question 12

A vector $\vec{A}$ has a magnitude of $5.00$ and points in a direction $40.0^\circ$ clockwise from the negative y-axis. What are the $x$ and $y$ components of $\vec{A}$?

Accepted Answer

$A_x = -3.21$, $A_y = 3.83$

Question 13

If $\vec{A} = 1.00\hat{i} + 4.00\hat{j}$, $\vec{B} = 3.00\hat{i} - 1.00\hat{j}$, and $\vec{C} = -1.00\hat{i} + 1.00\hat{j}$, what is the magnitude of $\vec{A} + \vec{B} + \vec{C}$?

Accepted Answer

$7.00$

Question 14

Given $\vec{A} = 1.00\hat{i} - 2.00\hat{j}$ and $\vec{B} = 3.00\hat{i} + 4.00\hat{j}$, what is the magnitude and direction of $\vec{C} = 3.00\hat{i} + 2.00\hat{j} - \vec{B}$?

Accepted Answer

$3.61$ in a direction $56.3^\circ$ counterclockwise from the positive x-axis

Question 15

If $\vec{A} = 3.90$ and $\vec{A}_y = -4.00$, what is the angle measured counterclockwise from the $x$-axis to vector $\vec{A}$?

Accepted Answer

$314^\circ$

Question 16

Given $\vec{A}_x = -3.5$, $\vec{A}_y = -9.7$, $\vec{C}_x = 6.4$, and $\vec{C}_y = +8.1$, what is the angle (less than $180^\circ$) between vectors $\vec{A}$ and $\vec{C}$?

Accepted Answer

$126^\circ$

Question 17

A ball is thrown with an impact velocity of $12.7\ \mathrm{m/s}$ straight downward onto a hill that slopes upward at $26^\circ$. What is the component of the ball's impact velocity parallel to the surface of the slope?

Accepted Answer

$8.7\ \mathrm{m/s}$

Question 18

If $\vec{A} = 16.0$ units and $\vec{B} = 7.00$ units, and the angle between them is $31.0^\circ$, what is the magnitude of $\vec{C} = \vec{A} - \vec{B}$?

Accepted Answer

$17.2$

Question 19

Which of the following is a true statement about vectors?

Accepted Answer

Rotating a vector about an axis passing through the tip of the vector does not change the vector.

Vectors: Concepts, Components, and Applications in Physics

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