Q: If a force $$\vec{F} is $$applied at an angle $$\theta to $$the direction of motion, the work done is:

$$|\vec{F}| |\vec{d}| \cos \theta$$

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 best describes a vector?

Accepted Answer

A quantity with 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

$$-4$$

Question 6

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

Accepted Answer

It is zero

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

Given $$\vec{u} = \langle 1, 2, 3 angle$$ and $$\vec{v} = \langle 4, 5, 6 angle$$, what is $$\vec{u} 	imes \vec{v}$$?

Accepted Answer

$$\langle -3, 6, -3 \rangle$$

Question 9

Which of the following statements about the cross product is correct?

Accepted Answer

The cross product of two vectors is a vector orthogonal to both

Question 10

If $$\vec{u} = \langle 2, 0, 0 angle$$ and $$\vec{v} = \langle 0, 3, 0 angle$$, what is $$|\vec{u} 	imes \vec{v}|$$?

Accepted Answer

$$6$$

Question 11

A vector field is best described as:

Accepted Answer

A function that assigns a vector to each point in space

Question 12

If $$\vec{u} = \langle 1, -3, 2 angle$$ and $$\vec{v} = \langle -2, 0, 1 angle$$ are orthogonal, what is $$	ext{proj}_{\vec{v}} \vec{u}$$?

Accepted Answer

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

Question 13

Which formula gives the magnitude of the vector $$\vec{v} = \langle v_1$, v_2$, v_3$ \rangle$$?

Accepted Answer

$$\sqrt{v_1$^2 + v_2$^2 + v_3$^2}$$

Question 14

A vector $$\vec{a} is $$parallel to $$\vec{b} if $$and only if:

Accepted Answer

$$\vec{a} = k\vec{b}$$ for some scalar $$k$$

Question 15

If a force $$\vec{F} is $$applied at an angle $$	heta to $$the direction of motion, the work done is:

Accepted Answer

$$|\vec{F}| |\vec{d}| \cos 	heta$$

Question 16

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

Accepted Answer

Dividing one vector by another

Question 17

If $$\vec{u} = \langle 3, 4, 0 \rangle$$ and $$\vec{v} = \langle 0, 0, 5 \rangle$$, what is the area of the parallelogram formed by $$\vec{u}$$ and $$\vec{v}$$?

Accepted Answer

$$25$$

Vectors and Vector Operations in Calculus (MA 261 Lesson 1 Study Notes)

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