$$\theta = \arctan\left(\frac{-2}{7}\right)$$

Question 1

Given two points $$A(3, 4)$$ and $$B(-2, 1)$$, what is the vector from $$A to$$ $$B in $$component form?

Accepted Answer

$$\vec{AB} = \langle -5, -3 \rangle$$

Question 2

If $$\vec{u} = \langle 4, -7 \rangle$$ and $$\vec{v} = \langle -2, 5 \rangle$$, what is $$\vec{u} + \vec{v}$$?

Accepted Answer

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

Question 3

Which of the following best describes the vector $$\vec{v} = \langle -3, 4 \rangle$$?

Accepted Answer

A vector pointing left and up

Question 4

What is the magnitude of the vector $$\vec{v} = \langle 6, 8 \rangle$$?

Accepted Answer

$$10$$

Question 5

If a vector $$\vec{u}$$ has initial point $$(1, 2)$$ and terminal point $$(4, 6)$$, what is $$\vec{u} in $$component form?

Accepted Answer

$$\langle 3, 4 \rangle$$

Question 6

A plane travels from point $$A(2, 3) to $$point $$B(7, 11). $$What is the displacement vector?

Accepted Answer

$$\langle 5, 8 \rangle$$

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

$$\langle 6, -8 \rangle$$

Question 9

A force vector $$\vec{F} = \langle 5, 12 \rangle is $$applied to an object. What is the magnitude of the force?

Accepted Answer

$$13$$

Question 10

If the vector $$\vec{v} = \langle x, y \rangle$$ has a magnitude of $$5$$ and $$x = 3$$, what is $$y$$?

Accepted Answer

$$4$$

Question 11

Which of the following vectors is perpendicular to $$\vec{u} = \langle 2, 5 \rangle$$?

Accepted Answer

$$\langle -5, 2 \rangle$$

Question 12

A boat moves from $$(0, 0) to$$ $$(6, 8). $$What is the distance traveled?

Accepted Answer

$$10$$

Question 13

If $$\vec{u} = \langle 7, -2 angle$$, what is the direction angle $$	heta of$$ $$\vec{u}$$ with respect to the positive $$x-$$axis?

Accepted Answer

$$	heta = \arctan\left(\frac{-2}{7}ight)$$

Question 14

Which of the following is the correct component form for a vector with initial point $$(a, b)$$ and terminal point $$(c, d)$$?

Accepted Answer

$$\langle c-a, d-b \rangle$$

Vectors in Component Form and Their Applications

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