Question 1

Given vectors $$\vec{u} = \langle 2, 3 \rangle$$ and $$\vec{v} = \langle -1, 4 \rangle$$, what is $$\vec{u} + \vec{v}$$?

Accepted Answer

$$\langle 1, 7 \rangle$$

Question 2

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

Accepted Answer

$$\langle 7, -10 \rangle$$

Question 3

Which of the following best describes the geometric interpretation of vector addition?

Accepted Answer

Placing the tail of the second vector at the head of the first vector and drawing the resultant from the tail of the first to the head of the second.

Question 4

Given $$\vec{w} = \langle -4, 2 \rangle$$, what is the magnitude $$|\vec{w}|$$?

Accepted Answer

$$\sqrt{20}$$

Question 5

If $$\vec{u} = \langle 3, 4 \rangle$$, what is the unit vector in the direction of $$\vec{u}$$?

Accepted Answer

$$\langle \frac{3}{5}, \frac{4}{5} \rangle$$

Question 6

A plane travels from point $$A(1,2) to $$point $$B(5,7). $$What is the displacement vector?

Accepted Answer

$$\langle 4, 5 \rangle$$

Question 7

If $$\vec{v} = \langle x, y \rangle$$ and $$|\vec{v}| = 10$$, which equation must be true?

Accepted Answer

$$x^2$$ + $$y^2 = 100$

Question 8

Which operation is NOT valid for vectors $$\vec{a}$$ and $$\vec{b} in $$component form?

Accepted Answer

Multiplying $$\vec{a}$$ and $$\vec{b}$$ component-wise to get a scalar.

Question 9

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

Accepted Answer

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

Question 10

A force of $$10 N $$acts at an angle of $$60^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$10 \cos 60^\circ$$

Question 11

Given $$\vec{a} = \langle 2, -3 \rangle$$ and $$\vec{b} = \langle -1, 4 \rangle$$, what is the result of $$\vec{a} + 3\vec{b}$$?

Accepted Answer

$$\langle -1, 9 \rangle$$

Question 12

If $$\vec{v} = \langle 7, 24 \rangle$$, what is $$|\vec{v}|$$?

Accepted Answer

$$25$$

Question 13

A boat moves $$3 km $$east and then $$4 km $$north. What is the magnitude of the displacement vector?

Accepted Answer

$$5 km$$

Question 14

Which of the following is the correct component form for a vector with magnitude $$8$$ and direction $$	heta = 30^\circ$$ above the positive $$x-$$axis?

Accepted Answer

$$\langle 8 \cos 30^\circ, 8 \sin 30^\circ \rangle$$

Question 15

If $$\vec{u} = \langle 0, 5 angle$$, what is the direction angle $$	heta ($$measured counterclockwise from the positive $$x-$$axis)?

Accepted Answer

$$90^\circ$$

Vectors: Representation and Operations in Component Form

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