Question

If `veca and vecb` are two non collinear unit vectors and `|veca+vecb|= sqrt3`, then find the value of `(veca- vecb)*(2veca+ vecb)`

Answer 1

Correct Answer - `(1)/(2)`
`because a=b = 1` so `a^(2) + b^(2) + 2ab cos theta = (sqrt3)^(2) = 3`
`rArr " "1+1 + 2cos theta = 3 rArr cos theta = (1)/(2)`
`( veca-vecb) *( 2veca+ vecb) = 2a^(2) - b^(2) - abcostheta`
`" "= 2-1- (1)/(2 )=(1)/(2)`