Free Printable Unit 8 Vector Quiz

1.

Find the component form of $\overrightarrow{\ v\ \ }$

a)

$<\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}>$

b)

$<\sqrt{2},\sqrt{2}>$

c)

$<\frac{3\sqrt{2}}{2},\frac{3\sqrt{2}}{2}>$

d)

$<\frac{\sqrt{3}}{2},\frac{1}{2}>$

e)

$<\sqrt{3},1>$

2.

Find the resultant of $\overrightarrow{\ v\ \ }+\overrightarrow{\ w\ \ }$

a)

$<\frac{2\sqrt{3}+3\sqrt{2}}{2},\frac{\ 3\sqrt{2}+1}{2}>$

b)

$<\frac{3\sqrt{3}+2\sqrt{2}}{2},\frac{\ 2\sqrt{2}+3}{2}>$

c)

$<\frac{\sqrt{2}+\sqrt{3}}{2},\frac{\sqrt{2}+1}{2}>$

d)

$<\frac{3\sqrt{3}+\sqrt{2}}{2},\frac{\sqrt{2}+3}{2}>$

3.

Given $\overrightarrow{\ a\ }=<-3,-6>$ and $\overrightarrow{\ b\ }=<4,-3>$ find $\overrightarrow{\ r\ }=3\overrightarrow{\ a\ }-2\overrightarrow{\ b\ }$ (Do not include spaces in your answer)

(a)

4.

Given $\overrightarrow{\ a\ }=<-3,-6>\ and\ \overrightarrow{\ b\ }=<4,-3>$ find the unit vector of $\overrightarrow{\ b\ }$ (Do not include spaces in your answers)

(a)

5.

Given $\overrightarrow{\ v\ }=<1,-1,1>and\ \overrightarrow{\ w\ }=<0,-3,2>$ find $\left|\left|\overrightarrow{\ v\ }\right|\right|+\left|\left|\overrightarrow{\ w\ }\right|\right|$ . Round your answer to the nearest hundredth place.

(a)

6.

Given $\overrightarrow{\ a\ }=<-3,-6>\ and\ \overrightarrow{\ b\ }=<4,-3>$ find $\left|\left|\overrightarrow{\ a\ }+2\overrightarrow{\ b\ }\right|\right|$

(a)

7.

Given $\overrightarrow{\ v\ }=<1,-1,1>and\ \overrightarrow{\ w\ }=<0,-3,2>$ find $\overrightarrow{\ v\ }\cdot\overrightarrow{\ w\ }$

(a)

8.

Given vectors $\overrightarrow{\ v\ }=<1,-1,1>and\ \overrightarrow{\ w\ }=<0,-3,2>$ find the angle between the two vectors. Round your answer to the nearest hundredth.

(a)

9.

Given the magnitude & direction of the resultant, find the horizontal & vertical components. Direction: 287° Magnitude: 422mph

a)

Horizontal -403.6
Vertical 123.4

b)

Horizontal 123.4
Vertical -403.6

c)

Horizontal 123.4
Vertical 403.6

d)

Horizontal -123.4
Vertical -403.6

10.

Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS.

a)

〈14,-13〉

b)

〈-14,13〉

c)

〈-40,-21〉

d)

〈40,-21〉

11.

Determine the direction and magnitude of the vector 〈7,18〉

a)

Direction 21.3°
Magnitude 19.3

b)

Direction 68.7°
Magnitude 19.3

c)

Direction 21.3°
Magnitude 373

d)

Direction 68.7°
Magnitude 373

12.

How do you know if two vectors are orthogonal?

a)

Their sum is 0.

b)

The dot product is 1.

c)

The angle between them is 0°.

d)

The dot product is 0.

13.

Write in component form.

a)

<0, 4>

b)

<8, 2>

c)

<2, 8>

d)

<0, 2>

14.

An airplane flying due south (270°) 485 mph against a 25 mph wind blowing due west(180°). Determine the new speed and direction of the plane.

a)

Direction 267.0°
Magnitude 485.6mph

b)

Direction 93.0°
Magnitude 485.6mph

c)

Direction 237.0°
Magnitude 485.6mph

d)

Direction 87.0°
Magnitude 510.0mph

15.

Find the angle between the two vectors:

a)

-0.789

b)

142.1

c)

100

d)

0.789

16.

A plane is flying at 650 mph on a course with bearing 285 ̊ and encounters a fierce wind blowing at 130 mph in the direction 330 ̊ . What is the component for of just the plane? (round answers to hundredths and do not include spaces)

(a)

17.

A plane is flying at 650 mph on a course with bearing 285 ̊ and encounters a fierce wind blowing at 130 mph in the direction 330 ̊ . What is the component for of just the wind? (round answers to hundredths and do not include spaces)

(a)

Unit 8 Vector Quiz

Total questions: 17

Worksheet time: 2hrs 18mins

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