Maths Quest C Year 11 for Queensland
WorkSHEET 7.1
Chapter 7 Introduction to vectors WorkSHEET 7.1
Introduction to vectors
1
Name: _________________________
2
1
(a)
AD  a~  b~  2 c~ or c~  e~  d
(b)
CF  2 c~  d~  e~
~
or
c~  a~  b~
From the figure above, express the following
vectors in terms of a~ , b~ , c~ , d~ and e~ .
(a) the vector from A to D.
(b) the vector from C to F.
(Give 2 answers for each vector).
2
A hiker travels 3 km north, then 4 km west.
How far is the hiker from the starting point?
What is the bearing of the resultant
displacement?
2
d  32  4 2
 5 km
4
tan 
3
  53.1
The hiker is 5 km from the starting point on a
bearing N 53.1 W or
(360 – 53.1)T = 306.9T.
Maths Quest C Year 11 for Queensland
3
Chapter 7 Introduction to vectors WorkSHEET 7.1
If u  4 i  7 j, find:
~
(a)
~
(a)
~
u
u  4i  7 j
~
~
u 
4 2   7 2
~
~
2
4
~
 16  49
(b)
 65
 8.06
u^
~
(b)
u^ 
~
u
~
u
~


4
Find the distance between the ends of the
vectors given by
a~  10 ~i  3 j and b~  5 ~i  9 j
~
~
4 i  7j
~
~
65
1 

 4 i  7 j 
65  ~
~
2
a~  b~  10 ~i  3 j   5 ~i  9 j 
~
~

 5 ~i  12 j
~
 5 2  12 2
 13
The distance is 13 units
5
Let u~  3 ~i  4 j  k~ and v~  2 ~i  3 j  3k~
~
Find u~ .v~
~
u~ . v~   3 ~i  4 j  k~ . 2 ~i  2 j  3k~ 
~
~



 683
 5
1
Maths Quest C Year 11 for Queensland
6
Chapter 7 Introduction to vectors WorkSHEET 7.1
u~ . v~  uv cos 
Find the angle between the vectors
u~  3 ~i  j and v~  4 ~i  3 j .
~
3
3
  3i  j  . 4 i  3 j 
 ~ ~ ~

~


~

 32  12
4 2   3 cos 
2
 12  3  10 25 cos 
 15  5 10 cos 
 15
cos  
5 10
3

10

  cos 1  

 161.6
3 

10 
The angle between u~ and v~ is approximately
161.6
7
Find the value of m if u~  2m ~i  3m j  4 k~ is
~
perpendicular to v~  ~i  2 j  3k~ .
~


 3
u . v   2m i  3m j  4 k . i  2 j  3 k 
~ ~
~
~
~
~
~

~

 2m  6m  12
 4m  12
u is at right angles to v if u . v  0
~
~
~ ~
 4m  12  0
4m  12
m3
8
If a~  ~i  2 j  k~ and b~  2 ~i  j  k~ calculate
~
9
2
~
(a)
2a~  b~
(a)
(b)
b~  2a~
(b)
A delivery boy travels 2 km north and then
3 km west and then another 2 km north.
(a) Use vectors to indicate these movements.
(b) Give the magnitude of his displacement
from his starting position.
6 i  3 j  3k
~
5 j k
~
(a)
~
2 j3i  2 j
~
~
(b)
~
~
~
  3 i 4 j
~
 5 km
~
2
Maths Quest C Year 11 for Queensland
10
Chapter 7 Introduction to vectors WorkSHEET 7.1
Calculate the dot product of the vectors shown
below.
a . b  a b cos
~ ~
~ ~
 2  5 cos(110  )
 3.42
4
1