Question 1

Which of the following statements about vector addition is correct based on the graphical methods shown in the images?

Accepted Answer

Vector addition is commutative, so $$\vec{A} + \vec{B} = \vec{B} + \vec{A}.$$

Question 2

Given vectors $$\vec{A}$$ and $$\vec{B}$$, which equation correctly represents the component method for finding the resultant vector $$\vec{R}$$?

Accepted Answer

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

Question 3

If $$\vec{A}$$ has a magnitude of 5 units and points along the positive x-axis, and $$\vec{B}$$ has a magnitude of 5 units and points along the positive y-axis, what is the magnitude of $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$5\sqrt{2}$$

Question 4

Which of the following best describes the effect of multiplying a vector $$\vec{A} by a $$scalar $$c = -2$$?

Accepted Answer

The new vector has twice the magnitude and the opposite direction as $$\vec{A}.$$

Question 5

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

Accepted Answer

$$8$$

Question 6

A pilot flies 100 km east, then 100 km north. What is the straight-line distance from the starting point to the final position?

Accepted Answer

$$100\sqrt{2} km$$

Question 7

Which of the following is true about the magnitude of the sum of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

It is always less than or equal to the sum of the magnitudes: $$|\vec{A} + \vec{B}| \leq |\vec{A}| + |\vec{B}|.$$

Question 8

If $$\vec{A}$$ points north and $$\vec{B}$$ points south with equal magnitudes, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

A zero vector.

Question 9

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

Accepted Answer

$$-2\hat{i} + 2\hat{j}$$

Question 10

A vector $$\vec{V}$$ has a direction of $$120^\circ. $$What is the direction of $$-\vec{V}$$?

Accepted Answer

$$300^\circ$$

Question 11

Which of the following is NOT a property of vector addition?

Accepted Answer

Non-commutativity

Question 12

If $$\vec{A} = 5\hat{i}$$ and $$\vec{B} = -3\hat{i}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$2\hat{i}$$

Question 13

A force vector $$\vec{F} is $$multiplied by a scalar $$c$$ with units of time (s). What is the physical interpretation of the new vector $$\vec{G} = c\vec{F}$$?

Accepted Answer

It is a vector with units of momentum.

Question 14

Which equation correctly expresses the magnitude of the resultant vector $$\vec{R}$$ when $$\vec{A}$$ and $$\vec{B}$$ are perpendicular?

Accepted Answer

$$|\vec{R}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2}$$

Question 15

If $$\vec{A} = 4\hat{i} + 3\hat{j}$$, what is the magnitude of $$-2\vec{A}$$?

Accepted Answer

$$2\sqrt{25}$$

Question 16

Which of the following best describes the result of multiplying a vector by zero?

Accepted Answer

A vector with zero magnitude and undefined direction.

Question 17

A displacement vector $$\vec{D} is $$tripled. What happens to its magnitude and direction?

Accepted Answer

The magnitude is tripled and the direction is unchanged.

Question 18

If $$\vec{A} = 6\hat{i} - 8\hat{j}$$, what is the unit vector in the direction of $$\vec{A}$$?

Accepted Answer

$$\frac{6}{10}\hat{i} - \frac{8}{10}\hat{j}$$

Question 19

Which of the following is a correct statement about vector subtraction?

Accepted Answer

$$\vec{A} - \vec{B} = \vec{A} + (-\vec{B})$$

Vector Arithmetic: Scalar Multiplication, Addition, and Subtraction

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