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Basic Vectors Review SHS

Total questions: 20

Worksheet time: 1hrs 4mins

Name
Class
Date
1.

Let u = <5, 2> and v = <1, -1>.


Find u + v.

a)

<4, -1>

b)

<6, 1>

c)

<3, 4>

d)

<1, 6>

2.
Given v = 〈3,-5〉 and w = 〈-2,3〉, what is w?
a)
〈6,-10〉
b)
〈1,-2〉
c)
〈0,-1〉
d)
none of these
3.

Let a = <-2, 0> and b = <-4, -8>.


Find a - b.

a)

<2, -8>

b)

<2, 8>

c)

<-6, -8>

d)

<-6, 8>

4.

If u = <-2, 0>, find 3u.

a)

<-6, 3>

b)

<-6, 0>

c)

<6, 0>

d)

<6, 3>

5.
If v =〈a,b〉, then a is the ___________ component of v.
a)
vertical
b)
horizontal
c)
parallel
d)
slope
6.

u + v

a)

4i - j

b)

6i + j

c)

3j + 4j

d)

i + 6j

7.
Given v = 〈3,-5〉 and w = 〈-2,3〉, what is w?
a)
〈6,-10〉
b)
〈1,-2〉
c)
〈0,-1〉
d)
none of these
8.
Find the dot product of <1, -2> and <3, 2>.
a)
1
b)
<3, -4>
c)
<4, 0>
d)
-1
9.
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.
10.

Find the magnitude of the vector <-4, 12>

a)

160\sqrt[]{160}  

b)

128\sqrt[]{128}  

c)

7

d)

17

11.
If the dot product of two vectors are equal to zero, then what do we know about the two vectors?
a)
They are parallel.
b)
They are orthogonal.
c)
They are neither.
12.

Given the initial and terminal points, determine component form.

IP = (2, -1), TP = (5, -3)

a)

<3, -2>

b)

<-3, 2>

c)

<-2, 3>

d)

<2, -3>

13.

Given the initial and terminal points, determine component form.

IP = (-3, 0), TP = (-2, -2)

a)

<-1, 2>

b)

<2, -1>

c)

<1, -2>

d)

<-2, 1>

14.

v - w

a)

-6i + 2j

b)

6i - 2j

c)

2i - 6j

d)

-2i + 6j

15.

Determine dot product, uvu\cdot v  

a)

-82

b)

-58

c)

82

d)

58

16.

If v =〈a,b〉, then b is the ___________ component of v.

a)

vertical

b)

horizontal

c)

parallel

d)

slope

17.

Determine the dot product given u = <4, 3> and v = <-5, -8>

(a)  

18.
If c=<-5, 4> and d=<8, 0>, calculate 2c+d
a)
<-2, 8>
b)
<-2, 0>
c)
<6, 8>
d)
<6, 0>
19.
Find the components of a vector v such that 
v + 
〈-6,4〉 = 〈10,-3〉
a)
〈4,1〉
b)
〈16,4〉
c)
〈16,-7〉
d)
none of these
20.

If IP = (-2, 5) and TP = (2, -8), find the component form.

a)

<4, 13>

b)

<-4, -13>

c)

<-4, 13>

d)

<4, -13>