If `veca+vecb=vec c` and a+b=c, what is the angle between `veca` and `vecb` ?

Options

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

Answer

D

Explanation

Here `veca+vecb=vecc` and c=a+b
Let `theta` be angle between `veca` and `vecb` .
`:. c = sqrt(a^(2)+b^(2)+2abcostheta)`
`a+b= sqrt(a^(2)+b^(2)+2ab cos theta)`
Squaring both sides we get
`(a+b)^(2) =a^(2)+b^(2) +2abcostheta`
`a^(2)+b^(2)+2ab=a^(2)+b^(2)+2abcostheta`
`2ab-2abcos theta=0 or 1-costheta=0`
`cos theta=1 or theta =cos^(-1) (1) =0^(@)`