Q: Which of the following is the correct formula for the vector (cross) product of $$\vec{A}$$ and $$\vec{B}$$?

$$|\vec{A} \times \vec{B}| = AB \sin \phi$$

Question 1

Which of the following best describes the difference between a physical law and a physical theory in physics?

Accepted Answer

A physical law is a well-established or widely used theory, while a physical theory is a pattern that relates phenomena in nature.

Question 2

A hospital MRI machine (as shown in the images) is an example of physics applied in which field?

Accepted Answer

Medicine

Question 3

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

Accepted Answer

Kilogram (kg)

Question 4

A measurement is recorded as 0.00203. How many significant figures does this value have?

Accepted Answer

3

Question 5

A train accident occurs due to a small percent error in the measurement of track length. This is an example of the importance of:

Accepted Answer

Accuracy

Question 6

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 7

Given two 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 8

A vector $$\vec{A}$$ has a magnitude of 5 units and makes an angle of $$30^\circ$$ with the x-axis. What is its x-component?

Accepted Answer

$$A_x = 5 \cos 30^\circ$$

Question 9

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 10

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

Accepted Answer

-5

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

$$\sqrt{(-3)^2$ + 4^2$}$$

Question 13

Which of the following is the correct formula for the vector (cross) product of $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$|\vec{A} 	imes \vec{B}| = AB \sin \phi$$

Question 14

Which of the following is a correct statement about unit vectors?

Accepted Answer

Unit vectors have a magnitude of 1 and indicate direction.

Question 15

A student adds two vectors $$\vec{A}$$ and $$\vec{B}$$ using the parallelogram method. Which statement is correct?

Accepted Answer

The resultant vector bisects the parallelogram formed by $$\vec{A}$$ and $$\vec{B}.$$

Question 16

Which of the following best describes a systematic error?

Accepted Answer

An error that is consistent and repeatable, often due to faulty equipment.

Question 17

A vector $$\vec{A} is $$multiplied by a scalar $$c = -2. $$Which of the following is true about the resulting vector?

Accepted Answer

The magnitude is doubled and the direction is reversed.

Question 18

Which of the following is the correct way to express a vector $$\vec{A} in $$terms of its components and unit vectors?

Accepted Answer

$$\vec{A} = A_x \hat{i} + A_y \hat{j}$$

Question 19

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

Accepted Answer

$$C_y = (A_z B_x - A_x B_z) = (1 	imes 1 - 2 	imes 4) = -7$$

Units, Physical Quantities, and Vectors – Foundations of Physics with Calculus

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