Question 1

Given two points $$P(2, -1, 3)$$ and $$Q(5, 2, 7)$$, what is the vector $$\overrightarrow{PQ}$$?

Accepted Answer

$$\langle 3, 3, 4 \rangle$$

Question 2

What is the magnitude of the vector $$\vec{v} = \langle 4, -3, 12 \rangle$$?

Accepted Answer

$$13$$

Question 3

If $$\vec{u} = \langle 1, 2, 3 \rangle$$ and $$\vec{v} = \langle 4, 5, 6 \rangle$$, what is $$\vec{u} + \vec{v}$$?

Accepted Answer

$$\langle 5, 7, 9 \rangle$$

Question 4

Which of the following statements about vectors is TRUE?

Accepted Answer

A vector has both magnitude and direction.

Question 5

Given $$\vec{u} = \langle 2, -1, 4 \rangle$$ and $$\vec{v} = \langle -1, 2, 0 \rangle$$, what is the dot product $$\vec{u} \cdot \vec{v}$$?

Accepted Answer

Question 6

If $$\vec{u} = \langle 1, -3, 2 \rangle$$ and $$\vec{v} = \langle -2, 0, 1 \rangle$$, what is the projection of $$\vec{u}$$ onto $$\vec{v}$$?

Accepted Answer

$$\langle 0, 0, 0 \rangle$$

Question 7

A force $$\vec{F} = \langle 10, 0 \rangle N $$moves an object 5 meters in the direction $$\langle 1, 0 \rangle. $$How much work is done?

Accepted Answer

$$50 J$$

Question 8

Which formula correctly gives the cross product $$\vec{u} 	imes \vec{v}$$ for $$\vec{u} = \langle u_1$, u_2$, u_3$ angle$$ and $$\vec{v} = \langle v_1$, v_2$, v_3$ angle$$?

Accepted Answer

$$\langle u_2$ v_3$ - u_3$ v_2$, u_3$ v_1$ - u_1$ v_3$, u_1$ v_2$ - u_2$ v_1$ \rangle$$

Question 9

If two nonzero vectors are orthogonal, what is true about their dot product?

Accepted Answer

It is zero.

Question 10

A vector field is best described as:

Accepted Answer

A function that assigns a vector to every point in space.

Question 11

Suppose $$\vec{u} = \langle 2, 0, 0 angle$$ and $$\vec{v} = \langle 0, 3, 0 angle. $$What is $$\vec{u} 	imes \vec{v}$$?

Accepted Answer

$$\langle 0, 0, 6 \rangle$$

Question 12

A vector $$\vec{a} is $$said to be a position vector if:

Accepted Answer

Its tail is at the origin and its head is at the point $$(a_1$, a_2$, a_3$).$$

Question 13

If $$\vec{u} = \langle 3, -2 \rangle$$ and $$c = -2$$, what is $$c\vec{u}$$?

Accepted Answer

$$\langle -6, 4 \rangle$$

Question 14

Which of the following best describes the physical meaning of the dot product in the context of work?

Accepted Answer

It gives the amount of force applied in the direction of motion times the distance moved.

Question 15

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

Accepted Answer

$$32$$

Question 16

Which of the following is NOT a valid vector operation in $$\mathbb{R}^3$$?

Accepted Answer

Multiplying two vectors to get a scalar using the cross product.

Vectors and Vector Operations: Foundations for Multivariable Calculus

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