Vectors Using i, j Notation

1
Vectors Using i, j Notation

• Understand the idea of i, j notation
• Add or subtract vectors in this form
• Find the magnitude of an i, j vector
• Change a vector given as a bearing or in polar
  form into i, j form

2
C
B
In i, j form, Vector AB 2i 5j Vector CD 1i
3j Vector EF -3i 1j
D
E
A
F
The i denotes a movement along the bottom axis
and the j the vertical axis. It looks complicated
but its just the same as the coordinate rule.
3
B
C
A
The vectors may be added like this VectorAB
VectorBC (2 1)i (5 -3)j
3i 2j VectorAC 3i 2j
4
B
C
A

• The vectors may be subtracted like this
• VectorAB VectorBC VectorAC
• VectorBC VectorAC VectorBC
• (3 - 2)i (2 - 5)j
• ? 1i -3j 1i - 3j

5
What is the magnitude of VectorAB if its I and j
components are 3i 4j
B
By Pythagoras the magnitude is v(32 42)
v25 5
A
6
N
Given that VectorAB has a magnitude of 5 and a
bearing of 0300, what are the i and j components?
B
0300
(5sin300) i (5cos300) j
A
7
N
VectorAB in polar form has a magnitude of 5 and
an angle of 600 5 lt600gt What are the i and j
components?
B
0600
(5cos600) i (5sin600) j
A