Q: If $$\vec{A} = 3\hat{i} + 4\hat{j}$$, what is the direction of $$\vec{A}$$ with respect to the positive x-axis?

$$\theta = \arctan\left(\frac{4}{3}\right)$$

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

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

Question 1

Which of the following best describes a vector quantity?

Accepted Answer

A quantity with both magnitude and direction.

Question 2

Given the vector $$\vec{v} = \begin{pmatrix} 1 \ 2 \end{pmatrix} as $$shown in the first image, what is its magnitude?

Accepted Answer

$$\sqrt{5}$$

Question 3

If $$\vec{A} = 3\hat{i} + 4\hat{j}$$, what is the direction of $$\vec{A}$$ with respect to the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{4}{3}ight)$$

Question 4

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 5

Given $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = -1\hat{i} + 4\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$1\hat{i} + 7\hat{j}$$

Question 6

If a vector $$\vec{A}$$ has components $$A_x = 5$$ and $$A_y = 12$$, what is its magnitude?

Accepted Answer

$$\sqrt{5^2$ + 12^2$}$$

Question 7

A vector $$\vec{B}$$ makes an angle of $$30^\circ$$ with the positive x-axis and has a magnitude of $$15 m. $$What is the y-component $$B_y$$?

Accepted Answer

$$B_y = 15 \sin 30^\circ$$

Question 8

Which of the following is NOT a property of unit vectors?

Accepted Answer

They have variable magnitude.

Question 9

If $$\vec{A} = A_x \hat{i} + A_y \hat{j}$$ and $$\vec{B} = B_x \hat{i} + B_y \hat{j}$$, what is the x-component of $$\vec{R} = \vec{A} + \vec{B}$$?

Accepted Answer

$$R_x = A_x + B_x$$

Question 10

A vector $$\vec{D} is $$defined as $$\vec{D} = \vec{A} - \vec{B}. $$Which statement is true?

Accepted Answer

$$\vec{D} is $$found by adding $$-\vec{B} to$$ $$\vec{A}.$$

Question 11

If a vector $$\vec{A} is $$multiplied by a scalar $$c$$, which of the following is true?

Accepted Answer

The magnitude of $$\vec{A} is $$scaled by $$|c|.$$

Question 12

Given $$\vec{A} = 0\hat{i} + (-8.00\,	ext{m})\hat{j}$$ and $$\vec{B} = (7.50\,	ext{m})\hat{i} + (13.0\,	ext{m})\hat{j}$$, what is the magnitude of $$\vec{A} + \vec{B}$$?

Accepted Answer

$$\sqrt{(7.50)^2$ + (5.0)^2$}$$

Question 13

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

Accepted Answer

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

Question 14

Which of the following is a scalar quantity?

Accepted Answer

Mass

Question 15

If $$\vec{A} is in $$the second quadrant, which of the following is true about its components?

Accepted Answer

$$A_x  0$$

Question 16

In three dimensions, which unit vector points in the z-direction?

Accepted Answer

$$\hat{k}$$

Question 17

A vector $$\vec{R} is $$the sum of $$\vec{A}$$ and $$\vec{B}. $$Which equation correctly represents the y-component of $$\vec{R}$$?

Accepted Answer

$$R_y = A_y + B_y$$

Question 18

If $$\vec{A}$$ and $$\vec{B}$$ are vectors, which of the following is true about their sum $$\vec{A} + \vec{B}$$?

Accepted Answer

It is always a vector.

Study Notes: Units, Physical Quantities, and Vectors (PHYS2325 Chapter 1)

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