Free Printable 8.3 Dot Product

1.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

2.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

3.

Find the angle between the two vectors:

a)

-0.789

b)

142.1

c)

100

d)

0.789

4.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

5.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

6.

Find the dot product of the given vectors:

a)

92

b)

0

c)

-92

d)

none of the above

7.

Find the angle between the two vectors <3, 4> and <4, -3>

a)

90°

b)

45°

c)

53.13°

d)

106.26°

8.

Find the angle between v and w

a)

21.8 degrees

b)

111.8 degrees

c)

68.2 degrees

9.

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.

10.

What type of quantity is produced by the dot product of two vectors?

a)

scalar

b)

vector

11.

What type of quantity is produced by the dot product of two vectors?

a)

scalar

b)

vector

12.

If the dot product of two vectors is equal to zero, then what do we know about the two vectors?

a)

They are parallel.

b)

They are orthogonal.

c)

They are neither.

13.

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.

14.

Given parallel vectors u and v. Answer ALL that apply

a)

their scalar product is zero

b)

their scalar product is either 1 or -1

c)

u is a scalar multiple of v

d)

magnitude of u equals the magnitude of v

15.

If ||v||= 8, ||w||=6 and the angle between them is θ = 240˚ $Find\ \overrightarrow{\ \ v}.\overrightarrow{\ \ w}$

a)

-24

b)

24

c)

48

d)

-48

16.

What operation you need to find an angle between two vectors?

a)

Dot product between the two vectors

b)

Dot product between the two vectors divide the magnitude of both vectors

c)

Cosine inverse of dot product between the two vectors divide the magnitude of both vectors

d)

Cross product between the two vectors

17.

What is the angle between two orthogonal vectors?

a)

180 degree

b)

90 degree

c)

60 degree

d)

45 degree

18.

If $\overrightarrow{\ \ a}=3i\ +5j+k\ \ and\ \overrightarrow{\ \ b}=2i+j+3k\ then\ \overrightarrow{\ \ a}\ .\overrightarrow{\ \ b}=$

a)

41

b)

12

c)

21

d)

14

19.

If $\overrightarrow{\ \ a\ }=5i-7j-2k\ is\ perpendicular\ to\ \overrightarrow{\ \ b}\ =2i\ +pj+3k\ then\ p\ =$

a)

6/4

b)

7/4

c)

4/6

d)

4/7

20.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

21.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

22.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

8.3 Dot Product - Part 1

Total questions: 22

Worksheet time: 41mins

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