What is meant by subtraction of vectors?

Explanation

For two non-zero vectors consider `vec(A) and vec(B)` that are inclined to each other at an angle `theta` , the difference `vec(A) - vec(B)` is obtained as follows . first obtain ` - vec(B)` as in figure (Subtraction of vectors) . The angle between `vec(A) and - vec(B)` is `180 - theta` .
The difference `vec(A) - vec(B)` is the same as the resultant of `vec(A) and - vec(B)`
We can write `vec(A) - vec(B) = vec(A) + (-vec(B)) ` and using the equation , we get
`|vec(A)- vec(B)| = sqrt(A^(2) +B^(2)+2A B cos (180 - theta))`
Since , cos `(180 - theta) = - cos theta `, we get
`|vec(A) - vec(B)| = sqrt(A^(2) +B^(2) - 2 ABcos theta)`
Again from the figure, and the equation similar to the equation
`tan alpha_(2) = (B sin ( 180^(@) - theta))/(A + B cos (180^(@)- theta))`
But , sin `(180^(@) - theta) = sin theta` hence we get
`:. tan alpha_(2) = (B sin theta)/(A - B cos theta)`