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 $$|\vec{A}| \u003e |\vec{B}|$$, 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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