If `vec(A) + vec(B) = vec(C )` and `A + B = C`, then the angle between `vec(A)` and `vec(B)` is :

Options

A. `90^(@)`
B. `180^(@)`
C. `120^(@)`
D. zero

Answer

D

Explanation

Since, `vec(a) + vec(b) = vec(c) and a +b= c`
`c^(2)= a^(2) + b^(2) + 2ab cos theta`
`theta= 0^(@)`
`c^(2)= a^(2) + b^(2) + 2ab [cos 0^(@) =1]`
`because a^(2) + b^(2) + 2ab = (a+b)^(2)`
`therefore c^(2)= (a+ b)^(2)`
`c= (a +b)`
Aliter:
`c_("max")= a+b`, when `theta= 0^(@)`