Q: Which of the following is NOT a property of the scalar (dot) product?

$$\vec{A} \cdot \vec{B} = \vec{A} \times \vec{B}$$

Question 1

Which of the following is the correct SI unit for mass?

Accepted Answer

kilogram (kg)

Question 2

A car is traveling at 90 km/h. What is its speed in meters per second (m/s)?

Accepted Answer

$$25\ \mathrm{m/s}$$

Question 3

Which of the following quantities is a vector?

Accepted Answer

Velocity

Question 4

A swimming pool contains $$20,000\ \mathrm{ft}^3 of $$water. How many cubic meters is this? (1 ft = 0.3048 m)

Accepted Answer

$$566\ \mathrm{m}^3$$

Question 5

Which of the following equations is dimensionally consistent for calculating distance $$x$$ traveled at constant velocity $$v$$ for time $$t$$?

Accepted Answer

$$x = vt$$

Question 6

A hiker walks $$4.0\ \mathrm{km}$$ east, then $$3.0\ \mathrm{km}$$ north. What is the magnitude of her displacement from the starting point?

Accepted Answer

$$5.0\ \mathrm{km}$$

Question 7

Which of the following best describes the right-hand rule for the cross product $$\vec{C} = \vec{A} 	imes \vec{B}$$?

Accepted Answer

Point your fingers in the direction of $$\vec{A}$$, curl toward $$\vec{B}$$, and your thumb points in the direction of $$\vec{C}.$$

Question 8

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

Accepted Answer

$$0$$

Question 9

A vector $$\vec{A}$$ has components $$A_x = 6$$ and $$A_y = 8. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$10$$

Question 10

Which of the following is NOT a property of the scalar (dot) product?

Accepted Answer

$$\vec{A} \cdot \vec{B} = \vec{A} 	imes \vec{B}$$

Question 11

A tape measure (like the one shown in the images) is used to measure the length of a table. Which physical quantity is being measured?

Accepted Answer

Length

Question 12

A digital scale (like the one shown in the images) reads 0 g when empty. What is the physical quantity measured by this device?

Accepted Answer

Mass

Question 13

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

Accepted Answer

$$\hat{i} + 7\hat{j}$$

Question 14

Which of the following is an example of a scalar quantity?

Accepted Answer

Temperature

Question 15

A vector $$\vec{V}$$ makes an angle $$	heta$$ with the x-axis. Which expression gives the x-component of $$\vec{V}$$?

Accepted Answer

$$V \cos 	heta$$

Question 16

A hiker walks $$5.0\ \mathrm{km}$$ southeast, then $$8.0\ \mathrm{km} at$$ $$30^\circ$$ east of north, then $$2.0\ \mathrm{km}$$ west. What is the total displacement from the starting point (magnitude only)?

Accepted Answer

$$6.5\ \mathrm{km}$$

Question 17

Which of the following is the correct result for the cross product $$\hat{i} 	imes \hat{j}$$?

Accepted Answer

$$\hat{k}$$

Question 18

Which of the following is NOT a correct rule for significant figures?

Accepted Answer

Always round intermediate results to one significant figure.

Question 19

Which of the following best describes the purpose of dimensional analysis?

Accepted Answer

To check the consistency of equations and units.

Chapter 1: Units, Physical Quantities, and Vectors – Study Notes

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