Choose the correct option:
The two vectors `vec(A)` and `vec(B)` are drawn from a common point and `vec(C)=vec(A)+vec(B)` then angle between `vec(A)` and `vec(B)` is

Options

A. `90^(@)` if `C^(2) ne A^(2)+B^(2)`
B. Greater than `90^(@)` if `C^(2) lt A^(2)+B^(2)`
C. Greater than `90^(@)` if `C^(2) gt A^(2)+B^(2)`
D. None of these

Answer

B

Explanation

`:' vec(C)=vec(A)+vec(B) :. C^(2)=A^(2)+B^(2)+2AB cos theta`
If `C^(2) lt A^(2) + B^(2)` then `cos theta lt 0`
Therefore `theta gt 90^(@)`