Question 1

Given a vector $$\vec{v} = \langle 3, 4 \rangle$$, what is the magnitude of $$\vec{v}$$?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5$$

Question 2

Which formula correctly calculates the magnitude of a vector $$\vec{v} = \langle a, b \rangle$$?

Accepted Answer

$$|\vec{v}| = \sqrt{a^2$ + b^2$}$$

Question 3

A displacement vector in a city grid is $$\vec{d} = \langle -6, 8 \rangle. $$What is the magnitude of this displacement?

Accepted Answer

$$\sqrt{(-6)^2$ + 8^2$} = 10$$

Question 4

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

Accepted Answer

$$\sqrt{(1+4)^2$ + (2+(-2))^2$} = \sqrt{25} = 5$$

Question 5

A vector $$\vec{a}$$ has components $$\langle x, y \rangle. If$$ $$|\vec{a}| = 13$$ and $$x = 5$$, what is $$y$$?

Accepted Answer

$$y = \sqrt{13^2$ - 5^2$} = \sqrt{169 - 25} = \sqrt{144} = 12$$

Question 6

Which of the following best describes the geometric meaning of the magnitude of a vector $$\vec{v} = \langle a, b \rangle$$?

Accepted Answer

It is the length of the vector from the origin to the point $$(a, b).$$

Question 7

A vector $$\vec{w}$$ has magnitude $$7$$ and points in the direction $$\langle 3, 4 \rangle. $$What is the unit vector in the direction of $$\vec{w}$$?

Accepted Answer

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

Question 8

A boat travels east for 6 km and then north for 8 km. What is the straight-line distance from its starting point?

Accepted Answer

$$\sqrt{6^2$ + 8^2$} = 10 km$$

Question 9

If $$\vec{p} = \langle x, y \rangle$$ and $$|\vec{p}| = \sqrt{50}$$, which of the following could be the values of $$x$$ and $$y$$?

Accepted Answer

$$x = 5, y = 5$$

Question 10

A vector $$\vec{q}$$ has components $$\langle -7, 24 \rangle. $$What is $$|\vec{q}|$$?

Accepted Answer

$$\sqrt{(-7)^2$ + 24^2$} = 25$$

Question 11

A drone flies 9 meters east and 12 meters north. What is the magnitude of its displacement vector?

Accepted Answer

$$\sqrt{9^2$ + 12^2$} = 15$$ meters

Question 12

If $$\vec{r} = \langle 0, y \rangle$$ and $$|\vec{r}| = 8$$, what is $$y$$?

Accepted Answer

$$y = 8$$

Question 13

Which of the following vectors has a magnitude of $$\sqrt{2}$$?

Accepted Answer

$$\langle 1, 1 \rangle$$

Question 14

A vector $$\vec{s}$$ has components $$\langle 8, 15 \rangle. $$What is $$|\vec{s}|$$?

Accepted Answer

$$\sqrt{8^2$ + 15^2$} = 17$$

Question 15

If $$\vec{t} = \langle a, b \rangle$$ and $$|\vec{t}| = 10$$, which equation must be true?

Accepted Answer

$$a^2$$ + $$b^2 = 100$

Question 16

A hiker walks 5 km west and 12 km south. What is the magnitude of the hiker's displacement?

Accepted Answer

$$\sqrt{5^2$ + 12^2$} = 13 km$$

Question 17

Which of the following is NOT a correct way to find the magnitude of $$\vec{v} = \langle a, b \rangle$$?

Accepted Answer

$$|\vec{v}| = a + b$$

Vectors in the Coordinate Plane: Magnitude and Applications

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