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Vectors!

Total questions: 20

Worksheet time: 2hrs 0mins

Name
Class
Date
1.
A vector is a mathematical structure that has both _______ and _______.
a)
direction, magnitude
b)
scope, sequence
c)
meat, potatoes
d)
scalar, vector
2.

Which are equivalent vectors?

a)

u and -u

b)

u and a

c)

u and v

d)

u and b

3.

Write in component form.

a)

<0, 4>

b)

<8, 2>

c)

<2, 8>

d)

<0, 2>

4.

What vector gives the sum of these two vectors?

a)
b)
c)
d)
e)
5.

Find the magnitude of the vector <10, -8>

a)

2

b)

12.81

c)

6

d)

18

6.

Find the magnitude of this vector (each square is 1 unit long)

a)

4

b)

5

c)

3

d)

square root of 5

7.

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〉

8.
Find the magnitude of vector AB if the initial point is (-3, 1) and the terminal point is (3, 9).
a)
6
b)
8.2
c)
10
d)
10.4
9.

Given u = <3, 7>, find 2u

a)

<21, 2>

b)

<6, 26>

c)

<6, 14>

d)

23

10.
Given u = <3, 7> and v =<-5, 4>, find 2v - 3u
a)
<21, 2>
b)
<-19, -13>
c)
<-15, 3>
d)
23
11.

If y = <2, 0> and z = <-1, -4>, find 3y - 2z.

a)

<5, -8>

b)

<4, 8>

c)

<8, 8>

d)

<-8, -8>

12.

Given points A(3, 2, -4) and B(2, 1, -1), find vector AB.

a)

< 1, 3, -5 >

b)

< -1, -3, 3>

c)

< 1, -1, -5 >

d)

< -1, -1, 3 >

13.
What direction is the angle?
a)
east of north
b)
south of east
c)
north of east
d)
west of east
14.

Describe the direction of the vector.

a)

20o east of south

b)

20o south of east

c)

20o south of west

d)

20o west of south

15.

Describe the direction of this vector.

a)

33o north of west

b)

33o west of north

c)

33o east of north

d)

33o north of east

16.

What's the x-component of the vector with magnitude 13, 55° North of East?

a)

10.64

b)

0.28

c)

7.45

d)

20

17.

Determine the components of the vector with magnitude 10, 60 degrees from the positive x-axis.

a)

<5, 8.7>

b)

<8.7, 5>

c)

<59.1, 10.4>

d)

<10.4, 59.1>

18.

Write the vector in component form.

a)

< 89.2, -80.3 >

b)

< 133.3, -80.3 >

c)

< -80.3, 89.2 >

d)

< 89.2, -133.3 >

19.

The vector with magnitude 5, 200° from the positive x-axis would be drawn in the _____ quadrant.

a)

first (I)

b)

second (II)

c)

third (III)

d)

fourth (IV)

20.

What's the y-component of the vector with a length of 8, 200° from the positive x-axis?

a)

-7.51

b)

2.73

c)

-2.73

d)

-6.98