Question 1

Which of the following best describes a vector?

Accepted Answer

A quantity with both magnitude and direction.

Question 2

Given the points $$P = (2,2)$$ and $$Q = (3,-1)$$, what is the vector $$\vec{PQ}$$?

Accepted Answer

$$\langle 1, -3 \rangle$$

Question 3

If $$\vec{a} = \langle 2,2 \rangle$$ and $$\vec{b} = \langle 1,-3 \rangle$$, what is $$\vec{a} + \vec{b}$$?

Accepted Answer

$$\langle 3, -1 \rangle$$

Question 4

Which property does vector addition satisfy?

Accepted Answer

Componentwise addition

Question 5

What is the result of multiplying the vector $$\vec{a} = \langle 2,1 \rangle by$$ $$-1$$?

Accepted Answer

$$\langle -2, -1 \rangle$$

Question 6

If $$\vec{a} = \langle 2,1 \rangle$$, what is $$3\vec{a}$$?

Accepted Answer

$$\langle 6,3 \rangle$$

Question 7

What is the magnitude of the vector $$\vec{v} = \langle 3,4 \rangle$$?

Accepted Answer

$$5$$

Question 8

Which formula gives the magnitude of a vector $$\vec{v} = \langle x, y \rangle$$?

Accepted Answer

$$\sqrt{x^2$ + y^2$}$$

Question 9

What is a unit vector?

Accepted Answer

A vector with length $$1$$

Question 10

Given two points $$P = (x_1$, y_1$)$$ and $$Q = (x_2$, y_2$)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 11

Which of the following is the zero vector?

Accepted Answer

$$\langle 0, 0 \rangle$$

Question 12

If $$\vec{a} = \langle 2,2 \rangle$$ and $$\vec{b} = \langle 1,-3 \rangle$$, what is $$\vec{a} - \vec{b}$$?

Accepted Answer

$$\langle 1, 5 \rangle$$

Question 13

Which of the following is a special unit vector in the $$x-$$direction?

Accepted Answer

$$\hat{i} = \langle 1, 0 \rangle$$

Question 14

If $$\vec{a} = \langle 2,1 \rangle$$, what is $$\frac{1}{2}\vec{a}$$?

Accepted Answer

$$\langle 1, \frac{1}{2} \rangle$$

Question 15

Which operation is used to describe the relative position between two points $$P$$ and $$Q$$?

Accepted Answer

The vector $$\vec{PQ}$$

Question 16

If $$\vec{a} = \langle 2,2 \rangle$$ and $$\vec{b} = \langle 1,-3 \rangle$$, which of the following is true?

Accepted Answer

$$\vec{a} + \vec{b} = \langle 3, -1 \rangle$$

Question 17

Which of the following statements about vector addition is correct?

Accepted Answer

Vector addition is componentwise.

Question 18

A drone moves from point $$A = (1,2) to $$point $$B = (4,6). $$What is the displacement vector?

Accepted Answer

$$\langle 3, 4 \rangle$$

Question 19

A rescue robot must travel from $$(0,0) to$$ $$(3,4). $$What is the minimum distance it must travel?

Accepted Answer

$$5$$

Vectors: Definitions, Operations, and Properties in Calculus

Study Guide - Practice Questions