Subtraction of Vectors
Since, 
or , equivalently 
This indicates that subtraction can be considered equivalent to ” addition of negetive of the second vector to the first vector”.
The magnitude of subtraction of vector is
……………….. [1]
The angle between the resultant and the first vector ‘α’ is given by
……………………………..[2]
Example 1. A motorcyclist moving towards East with speed 20 km/hr takes a sharp turn and then moves towards North keeping his speed unchanged. Determine the change in his velocity.
Solution. Since the speed remains the same
or 
km/hr = 20 × 1.414 km/hr = 28.28 km/hr
Again, from fig 
or α = 450
Thus, the change in velocity of the motorcyclist is 28.28 km/hr, 450 West of North.
Example 2. Two vectors 
and 
are such that it satisfies the conditions 
. Determine the angle between and .
Solution. 
Squaring (i) and (ii)
then cos θ = 0 or θ = 900
Example 3. Two vectors and of same magnitude when added the resultant is also a vector of same magnitude. Determine the angle between the vectors and .
Solution.
x2 = x2 + x2 + 2.x.x.cos θ
x2 = 2x2 + 2x2.cos θ
1 = 2 + 2 cos θ
cos θ = or cos θ = – cos 600 or cos θ = cos (180 – 60)
θ = 180 – 600 or θ = 1200
Example 4. Sum of two vectors and is such that it is perpendicular to one of the vector and its magnitude is half of the larger vector. Determine the angle between two given vectors.
Solution.
Consider the figure. It is given that
So, the angle between the vectors = 1800 – α
θ = 1800 – 300 or θ = 1500
