If `veca and vecb` are unequal unit vectors such that `(veca - vecb) xx[ (vecb + veca) xx (2 veca + vecb)] = veca+vecb` then angle `theta " between " veca and vecb` is

Options

A. 0
B. `pi//2`
C. `pi//4`
D. `pi`

Answer

b,d

Explanation

`(vecaxxvecb)xx[(vecb+veca)xx (2veca+ vecb)] = vecb+veca`
`or {(veca-vecb).(2veca+vecb) } (vecb +veca) `
`-{(veca-vecb). (vecb+veca)}(2veca + vecb)= vecb+veca`
`or (2-veca.vecb- 1) (vecb +veca) = veca.vecb=1`
`Rightarrow "either " vecb +veca =vec0 or 1 - veca.vecb=1`
`Rightarrow "either " vecb = -veca or veca.vecb=0`
`Rightarrow "either " theta= pi" "theta = pi//2`