Question 1

Given vectors $$\vec{a}$$ and $$\vec{b} as $$shown on the graph, which of the following best represents the resultant vector $$\vec{a} + \vec{b}$$?

Accepted Answer

A vector starting at the origin and ending at the tip of $$\vec{b}$$ after $$\vec{a} is $$drawn.

Question 2

Given vectors $$\vec{a}$$ and $$\vec{b}$$, which of the following best represents the resultant vector $$-2\vec{a} + 3\vec{b}$$?

Accepted Answer

A vector that is twice as long as $$\vec{a} in $$the opposite direction, added to three times $$\vec{b}.$$

Question 3

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

Accepted Answer

$$\langle 1, 7 \rangle$$

Question 4

If $$\vec{a} = \langle 1, 2 \rangle$$ and $$\vec{b} = \langle 3, -1 \rangle$$, what is $$-2\vec{a} + 3\vec{b}$$?

Accepted Answer

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

Question 5

Which of the following statements about vector addition is correct?

Accepted Answer

Vector addition is commutative: $$\vec{a} + \vec{b} = \vec{b} + \vec{a}.$$

Question 6

If $$\vec{a} = \langle 4, -2 \rangle$$ and $$\vec{b} = \langle -1, 5 \rangle$$, what is the magnitude of $$\vec{a} + \vec{b}$$?

Accepted Answer

$$\sqrt{29}$$

Question 7

A pilot flies 100 km east and then 100 km north. What is the magnitude of the resultant displacement?

Accepted Answer

$$100\sqrt{2} km$$

Question 8

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

Accepted Answer

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

Question 9

Which operation results in a vector with the same direction as $$\vec{a}$$ but twice the magnitude?

Accepted Answer

$$2\vec{a}$$

Question 10

If $$\vec{a} = \langle 1, 2 \rangle$$ and $$\vec{b} = \langle 2, 1 \rangle$$, what is the dot product $$\vec{a} \cdot \vec{b}$$?

Accepted Answer

$$4$$

Conic Sections: Identifying Parabolas and Hyperbolas

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