LAWS OF VECTORS – ADDITION
A: TRIANGULAR LAW OF VECTORS APPLICATION
Consider the vector diagram below;
+ 
– 
= 0
= 
+ 
+ 
Where r is the resultant vector
B. PARALLELOGRAM LAW OF VECTORS ADDITION
– Consider the vector diagram below
+ 
= 
…………………………(i)
+ 
– 
= 0
+ 
= 
……………………………(ii)
From (i) and (ii) above
Proved
(ii) Addition of vectors is associative for any three vectors a, b and c
Proof
Consider the vector diagram below;
Individual but not considered
–
= 
= 
= 
……(i)
…………………..(ii)
From (i) and (ii) above
= 
Proved
(iii) For….. of additive identity
For every vector a, we have;
Where;
0 
The null (zero) vector
(iv) Entrance of addictive reverse
For every vector a we have
Where
→ is the positive of vector
→ is the null vector
ii. SUBTRACTION OF VECTORS
Suppose two dimensional vectors
Hence
= 
= 
– Suppose three dimensional vectors
Hence
Question 1
1. If 
(a Find (i) 
(ii) 
Comment of the results in (a) above
Question 2
Given that
(i) Find 
(ii) 
(b) Comment on the results in a above
MAGNITUDE OF A VECTOR
– The magnitude of a vector is a measure of length of the vector.
– – This is denoted by the symbol 
(a) Consider two dimensional vector
By using Pythagoras theorem
Recall;
Where
– is the magnitude/ module of the vector r
(b) Consider three dimensional vector 
RECTANGULAR RESOLUTION OF A VECTOR
Let: 
be three rectangular axes and 
be three unit vectors parallel to 
axes respectively.
Consider 
+
+ 
Also consider the right angled OFP
Using Pythagoras theorem
i.e a2 + b2 = c2
Where
= is the magnitude of the vector 
Question
Given that
Find 