Q: Which of the following statements about the cross product of two vectors $$\vec{A}$$ and $$\vec{B} is $$correct?

$$\vec{A} \times \vec{B} is $$perpendicular to both $$\vec{A}$$ and $$\vec{B}$$

Q: A vector $$\vec{E}$$ has a magnitude $$E$$ and makes an angle $$\theta$$ with the $$+x-$$axis. What are its $$x$$ and $$y$$ components?

$$E_x = E \cos \theta$$, $$E_y = E \sin \theta$$

Q: Which of the following is the correct way to convert 3.0 minutes to seconds?

$$3.0 \times \frac{60\ \text{s}}{1\ \text{min}} = 180\ \text{s}$$

Question 1

Which of the following is NOT a fundamental quantity in the International System of Units (SI)?

Accepted Answer

Force

Question 2

A rock has a mass of $$1.80 	imes 10^3$ kg and a volume of 6.0$$ 	imes $$10^{-2} m$^3. $$What is its density in SI units, expressed with the correct number of significant figures?

Accepted Answer

$$3.0 	imes 10^4$ kg/m^3$

Question 3

Which of the following best describes a scalar quantity?

Accepted Answer

A quantity with only magnitude

Question 4

A vector $$\vec{A}$$ has components $$A_x = -20.0 m $$and is directed $$40.0^\circ$$ clockwise from the $$+y-$$axis. What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$31.0 m$$

Question 5

Which of the following is the correct expression for the scalar (dot) product of two vectors $$\vec{A}$$ and $$\vec{B} in $$terms of their components?

Accepted Answer

$$A_x B_x + A_y B_y + A_z B_z$$

Question 6

A student walks 3.0 km east and then 4.0 km north. What is the magnitude of the resultant displacement?

Accepted Answer

$$5.0 km$$

Question 7

Which of the following statements about the cross product of two vectors $$\vec{A}$$ and $$\vec{B} is $$correct?

Accepted Answer

$$\vec{A} 	imes \vec{B} is $$perpendicular to both $$\vec{A}$$ and $$\vec{B}$$

Question 8

If $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and $$\vec{B} = -8\hat{i} + 6\hat{j}$$, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$48$$

Question 9

Which of the following is the correct result for the cross product $$\vec{A} 	imes \vec{B}$$, where $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and $$\vec{B} = -8\hat{i} + 6\hat{j}$$?

Accepted Answer

$$50\hat{k}$$

Question 10

A measurement is recorded as $$0.00340 kg. $$How many significant figures does this value have?

Accepted Answer

4

Question 11

Which of the following best describes the purpose of using idealized models in physics?

Accepted Answer

To simplify the analysis by ignoring less significant factors

Question 12

A vector $$\vec{E}$$ has a magnitude $$E$$ and makes an angle $$	heta$$ with the $$+x-$$axis. What are its $$x$$ and $$y$$ components?

Accepted Answer

$$E_x = E \cos 	heta$$, $$E_y = E \sin 	heta$$

Question 13

Which of the following is a correct statement about the addition of vectors graphically?

Accepted Answer

Vectors can be added in any order using the head-to-tail method

Question 14

A car travels 1.00 gigasecond ($$1.00 	imes 10^9$ s). Approximately how many years is this, assuming a 365-day year?

Accepted Answer

31.7 years

Question 15

Which of the following is the correct way to convert 3.0 minutes to seconds?

Accepted Answer

$$3.0 	imes \frac{60\ 	ext{s}}{1\ 	ext{min}} = 180\ 	ext{s}$$

Question 16

If two vectors $$\vec{A}$$ and $$\vec{B}$$ are perpendicular, what is the value of their dot product $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

It is zero

Question 17

Which of the following is a correct statement about significant figures in multiplication and division?

Accepted Answer

The answer should have as many significant figures as the number with the fewest significant figures

Question 18

Which of the following is the correct result for the cross product $$\vec{A} 	imes \vec{B} if$$ $$\vec{A}$$ and $$\vec{B}$$ are parallel?

Accepted Answer

It is the zero vector

Question 19

A unit vector is defined as:

Accepted Answer

A vector with magnitude 1 and a specified direction

Units, Physical Quantities, and Vectors – Study Notes

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