Q: Which equation represents the scalar (dot) product of two vectors $$\\vec{A}$$ and $$\\vec{B}$$?

$$\\vec{A} \\cdot \\vec{B} = AB \\cos \\phi$$

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

$$A_x = A \\cos \\theta, A_y = A \\sin \\theta$$

Q: Which of the following is true about the vector (cross) product $$\\vec{A} \\times \\vec{B}$$?

It is anticommutative: $$\\vec{A} \\times \\vec{B} = -\\vec{B} \\times \\vec{A}$$

Q: A vector $$\\vec{A}$$ has components $$A_x = -2$$ and $$A_y = 3. $$What is the direction angle $$\\theta$$ relative to the x-axis?

$$\\theta = \\tan$$^{-1}$$(3/-2)$$

Q: Which of the following is dimensionally consistent?

$$2\ \text{kg} + 4\ \text{kg}$$

Question 1

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

Accepted Answer

Temperature

Question 2

A physicist measures the mass of a paper clip as 0.5 g. What is this mass in kilograms?

Accepted Answer

$$0.0005\ 	ext{kg}$$

Question 3

Which step in the four-step physics problem-solving strategy involves checking your answer for reasonableness?

Accepted Answer

Evaluate your answer

Question 4

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 5

Which of the following statements about vector addition is correct?

Accepted Answer

The sum of two vectors is independent of the order in which they are added

Question 6

A cross-country skier travels 1.00 km north and then 2.00 km east. What is her resultant displacement?

Accepted Answer

$$2.24\ 	ext{km}$$

Question 7

If a vector $$\vec{A} is $$multiplied by a negative scalar $$-3$$, what happens to the vector?

Accepted Answer

Its magnitude triples and its direction reverses

Question 8

Which equation represents the scalar (dot) product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos \phi$$

Question 9

A vector $$\vec{A}$$ makes an angle $$\theta$$ with the x-axis. What are its x- and y-components?

Accepted Answer

$$A_x = A \cos \theta, A_y = A \sin \theta$$

Question 10

Which of the following is true about the vector (cross) product $$\vec{A} \times \vec{B}$$?

Accepted Answer

It is anticommutative: $$\vec{A} \times \vec{B} = -\vec{B} \times \vec{A}$$

Question 11

A train accident occurred due to a small percent error in measurement. Which concept does this illustrate?

Accepted Answer

The importance of significant figures and uncertainty in measurements

Question 12

If $$\vec{A}$$ and $$\vec{B}$$ are perpendicular, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$0$$

Question 13

Which of the following is a unit vector?

Accepted Answer

$$\vec{i}$$ with magnitude 1

Question 14

A vector $$\vec{A}$$ has components $$A_x = -2$$ and $$A_y = 3. $$What is the direction angle $$\theta$$ relative to the x-axis?

Accepted Answer

$$\theta = \tan$$^{-1}$$(3/-2)$$

Question 15

Which of the following is NOT a property of scalar quantities?

Accepted Answer

They have direction

Question 16

If $$\vec{A}$$ and $$\vec{B}$$ are parallel, what is the magnitude of their vector sum $$\vec{C}$$?

Accepted Answer

$$C = A + B$$

Question 17

Which method is most accurate for adding vectors?

Accepted Answer

Using vector components

Question 18

A vector $$\vec{A} is $$expressed as $$\vec{A} = A_x \vec{i} + A_y \vec{j}. $$What are $$\vec{i}$$ and $$\vec{j}$$?

Accepted Answer

Unit vectors in the x- and y-directions

Question 19

Which of the following is dimensionally consistent?

Accepted Answer

$$2\ 	ext{kg} + 4\ 	ext{kg}$$

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

Study Guide - Practice Questions

Study Guide - Flashcards