Q: Which of the following is the correct formula for the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$ given their magnitudes and the angle $$\theta$$ between them?

$$\vec{A} \cdot \vec{B} = |A||B|\cos(\theta)$$

Question 1

Which of the following quantities is a vector?

Accepted Answer

Displacement: $$10\,m$$ east

Question 2

A person walks $$3\,m to $$the right and then $$4\,m up. $$What is the magnitude of their total displacement?

Accepted Answer

$$5\,m$$

Question 3

A box is pushed by two perpendicular forces: $$12\,N to $$the right and an unknown force upward. If the total force is $$13\,N$$, what is the magnitude of the upward force?

Accepted Answer

$$5\,N$$

Question 4

A delivery truck travels $$8$$ miles east, $$5$$ miles north, and $$4$$ miles east again. What is the magnitude of its final displacement from the origin?

Accepted Answer

$$13\,miles$$

Question 5

Given $$\vec{A} = 8\,m (x-$$component), $$\vec{A}_y = 6\,m$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$10\,m$$

Question 6

A vector $$\vec{F} is$$ $$65\,m$$ long, directed $$30.5^{\circ}$$ below the positive x-axis. What is the y-component $$F_y$$?

Accepted Answer

$$F_y = -65 \sin(30.5$$^{\circ}$$)$$

Question 7

Which of the following is the correct formula for the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$ given their magnitudes and the angle $$	heta$$ between them?

Accepted Answer

$$\vec{A} \cdot \vec{B} = |A||B|\cos(	heta)$$

Question 8

Given $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = \hat{i} + 2\hat{j}$$, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$8$$

Question 9

If $$\vec{A} = 4\hat{i} + 3\hat{j}$$ and $$\vec{B} = -2\hat{i} + 3\hat{j}$$, what is the magnitude of $$\vec{C} = \vec{A} 	imes \vec{B}$$?

Accepted Answer

$$18$$

Question 10

Two vectors $$\vec{A}$$ and $$\vec{B}$$ have a scalar product of $$-8$$ and a vector product of magnitude $$12. $$What is the angle between them?

Accepted Answer

$$123.7^{\circ}$$

Question 11

A helicopter travels $$225\,m at$$ $$53.1^{\circ}$$ south of east. What is the x-component of its displacement?

Accepted Answer

$$225 \cos(53.1$$^{\circ}$$)$$

Question 12

Which statement about the cross product $$\vec{A} 	imes \vec{B} is $$correct?

Accepted Answer

It results in a vector perpendicular to both $$\vec{A}$$ and $$\vec{B}.$$

Question 13

Given $$\vec{A} = 7.2\hat{i} - 3.9\hat{j}$$ and $$\vec{B} = 2.1\hat{i} + 4.8\hat{j}$$, what is the dot product $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$1.44$$

Question 14

Which of the following best describes a unit vector?

Accepted Answer

A vector with magnitude 1 pointing in a specific direction.

Question 15

If $$\vec{A} = (4.0\,m)\hat{i} + (3.0\,m)\hat{j}$$ and $$\vec{B} = (-13.0\,m)\hat{i} + (7.0\,m)\hat{j}$$, what is $$\vec{C} = \vec{A} + \vec{B} in $$unit vector notation?

Accepted Answer

$$(-9.0\,m)\hat{i} + (10.0\,m)\hat{j}$$

Vectors: Concepts, Operations, and Applications

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