Question 1

Given vectors $$\vec{a} = \langle 3, -5, 2 \rangle$$ and $$\vec{b} = \langle 1, 4, -7 \rangle$$, what is $$\vec{a} + \vec{b}$$?

Accepted Answer

$$\langle 4, -1, -5 \rangle$$

Question 2

If $$\vec{v} = \langle 2, -3, 6 \rangle$$, what is the magnitude $$|\vec{v}|$$?

Accepted Answer

$$7$$

Question 3

Which of the following is the correct component form of the vector from point $$A(1, 2, 3) to $$point $$B(4, 0, -1)$$?

Accepted Answer

$$\langle 3, -2, -4 \rangle$$

Question 4

A plane travels from $$P(2, 5, 1) to$$ $$Q(-1, 3, 4). $$What is the displacement vector?

Accepted Answer

$$\langle -3, -2, 3 \rangle$$

Question 5

Given $$\vec{a} = \langle 2, -1, 3 \rangle$$ and $$\vec{b} = \langle -4, 0, 5 \rangle$$, what is $$\vec{a} - \vec{b}$$?

Accepted Answer

$$\langle 6, -1, -2 \rangle$$

Question 6

If $$\vec{u} = \langle 1, 2, 2 \rangle$$, what is the unit vector in the direction of $$\vec{u}$$?

Accepted Answer

$$\langle \frac{1}{3}, \frac{2}{3}, \frac{2}{3} \rangle$$

Question 7

A force vector $$\vec{F} = \langle 6, -8, 0 \rangle N $$acts on an object. What is the magnitude of the force?

Accepted Answer

$$10 N$$

Question 8

Which of the following vectors is perpendicular to $$\vec{a} = \langle 2, 1, 0 \rangle$$?

Accepted Answer

$$\langle -1, 2, 0 \rangle$$

Question 9

Given $$\vec{a} = \langle 3, -4, 0 \rangle$$, what is the direction cosine with respect to the $$x-$$axis?

Accepted Answer

$$\frac{3}{5}$$

Question 10

A drone moves from $$A(0, 0, 0) to$$ $$B(5, 12, 0). $$What is the distance traveled?

Accepted Answer

$$13$$

Question 11

If $$\vec{a} = \langle 1, 2, 3 \rangle$$ and $$\vec{b} = \langle 4, 5, 6 \rangle$$, what is $$\vec{a} \cdot \vec{b}$$?

Accepted Answer

$$32$$

Question 12

Which of the following is the correct formula for the magnitude of a vector $$\vec{v} = \langle a, b, c \rangle$$?

Accepted Answer

$$\sqrt{a^2$ + b^2$ + c^2$}$$

Vectors in Component Form: Concepts and Examples

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