Let a and b be unit vectors inclined at an angle `2alpha(0lealphalepi)` each other, then (a+b) `lt` 1, if

Options

A. `alpha=(pi)/(2)`
B. `alphalt(pi)/(3)`
C. `alphagt(2pi)/(3)`
D. `(pi)/(3)ltalphalt(2pi)/(3)`

Answer

D

Explanation

Given , `(a+b)lt 1`
` implies sqrt(1+12cos 2 alpha )lt 1`
` implies sqrt(2(1+cos 2 alpha ))lt 1`
`implies sqrt(4 cos ^(2) alpha )lt 1`
`implies | cos alpha |lt (1)/(2)`
`implies (pi)/(3)lt alpha lt (2pi)/(3) [ :' 0 le alpha le pi ]`