Vector Subtraction

Vector Subtraction is a special case of vctor addition. 
Let there are two Vectors A and B then subtraction of Vector B from A is A – B which can also be written as A + (-B).
So, A – B = A + (-B)
Here (–B) is a Vector that is parallel to Vector B but is in reverse or opposite direction of Vector B.
According to parallelogram law of addition, if there are two Vectors such that they form the two consecutive sides of a parallelogram then the sum of the Vectors is represented by the diagonal of the parallelogram passing through the point at which the tails of two Vectors meet. The geometrical representation of A-B is given in following diagram.

The above method is known as head to tail method.
You can find Subtraction of Vectors by using perpendicular components method. In this method you need to split each Vector into perpendicular components. We normally split the Vectors in x and y directions.
Suppose a Vector of magnitude 5 makes an angle of 30o with horizontal then its vertical component will be 5sin(30)j and horizontal component will be 5cos(30)i. i and j are unit Vectors along the x and y directions respectively. If a component is in downward or left direction assign a negative sign to it. Similarly Split all the given Vectors in such a way. Now add all the horizontal components together and add all the vertical components separately. Subtract a component if its magnitude is negative. Now calculate the resultant magnitude of the Vectors using Pythagoras theorem R2 = A2 + B2 . Here A is sum of horizontal components, B is sum of vertical components and R is resultant.
The angle that the resultant Vector makes with the horizontal is given as: Ө = tan-1|B|/|A|  . Here|A| and |B| are magnitudes of the Vectors.
Subtracting Vectors is similar to addition of Vector. The difference is just of the negative sign.
Let us see some Vector Subtraction Examples now:
Example 1) Subtract Vector B = 9i+7j+2k from A =3i + 5j + k.
Solution) To subtract B from A we write them as A-B = (3i + 5j + k) – (9i - 7j + 2k)
Now add the Vectors in the direction i, j, k separately. As the given Vectors are three dimensional we are considering z direction also. i, j, k refers to unit Vectors in x, y and z direction.
(3-9)i = -6i
(5- (-7))j= 12j
And (1-2)k = -k
A-B=(-6i+12j-k)
|A-B| = √(〖(-6)〗^2+〖12〗^2+〖(-1)〗^2 ) =√(36+144+1) = √181