Q: Which of the following is the correct formula for the cross product $$\vec{A} \times \vec{B} in $$terms of components?

$$\vec{A} \times \vec{B} = (A_y B_z - A_z B_y)\hat{i} + (A_z B_x - A_x B_z)\hat{j} + (A_x B_y - A_y B_x)\hat{k}$$

Q: A vector $$\vec{A}$$ makes an angle $$\theta$$ with the positive $$x-$$axis. Which of the following correctly gives its $$x$$ and $$y$$ components?

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

Question 1

Which of the following best describes the difference between a scalar and a vector quantity?

Accepted Answer

A vector has both magnitude and direction, while a scalar has only magnitude.

Question 2

A physicist measures the length of a rod as $$12.30 cm. $$How many significant figures does this measurement have?

Accepted Answer

4

Question 3

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

Accepted Answer

kilogram (kg)

Question 4

A car travels $$60.0 km in$$ $$1.50$$ hours. What is its average speed in meters per second ($$\mathrm{m/s}$$)?

Accepted Answer

$$11.1\ \mathrm{m/s}$$

Question 5

Which of the following statements about uncertainty is correct?

Accepted Answer

Random errors can be reduced by taking more measurements.

Question 6

Given vectors $$\vec{A}$$ and $$\vec{B}$$, which equation correctly represents their vector sum using components?

Accepted Answer

$$\vec{R} = (A_x + B_x)\hat{i} + (A_y + B_y)\hat{j}$$

Question 7

If $$\vec{A} = 3\hat{i} + 4\hat{j}$$, what is the magnitude $$|\vec{A}|$$?

Accepted Answer

$$5$$

Question 8

Which of the following is the correct formula for 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 $$\vec{A}$$ has components $$A_x = -6$$ and $$A_y = 8. $$What is the direction angle $$	heta ($$measured counterclockwise from the positive $$x-$$axis)?

Accepted Answer

$$127^\circ$$

Question 10

Which of the following is a correct statement about multiplying a vector by a scalar?

Accepted Answer

Multiplying by a negative scalar reverses the direction and changes the magnitude.

Question 11

Which of the following is the correct formula for the cross product $$\vec{A} 	imes \vec{B} in $$terms of components?

Accepted Answer

$$\vec{A} 	imes \vec{B} = (A_y B_z - A_z B_y)\hat{i} + (A_z B_x - A_x B_z)\hat{j} + (A_x B_y - A_y B_x)\hat{k}$$

Question 12

A measurement is recorded as $$0.00450 kg. $$How many significant figures does this value have?

Accepted Answer

3

Question 13

Which of the following is an example of a systematic error?

Accepted Answer

A scale that is improperly zeroed, always reading 0.5 kg too high.

Question 14

Which prefix represents $$10^{-9} in $$the SI system?

Accepted Answer

nano-

Question 15

A vector $$\vec{A}$$ makes an angle $$	heta$$ with the positive $$x-$$axis. Which of the following correctly gives its $$x$$ and $$y$$ components?

Accepted Answer

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

Question 16

Which of the following real-world technologies is most directly based on the physics of vectors and magnetic fields?

Accepted Answer

MRI (Magnetic Resonance Imaging)

Question 17

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

Accepted Answer

$$6$$

Question 18

A student adds $$24.5$$ and $$0.32. $$According to the rules for significant figures, what is the correct result?

Accepted Answer

$$24.8$$

Question 19

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

Accepted Answer

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

Chapter 1: Units, Physical Quantities, and Vectors – Physics with Calculus

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