If `bara` & `barb` are any two unit vectors then possible integers in the range of `(3|bara+barb|)/2+2|bara-barb|` is

Options

A. 2
B. 3
C. 4
D. 5

Answer

B, C, D

Explanation

Let angle between `bara` & `barb` be `theta|bara|=|barb|=1, (theta)/2`
`|bara+barb|=2"cos"(theta)/2`
`|bara-barb|=2"sin"(theta)/2`
`F(theta)=3/2 (2 "cos" (theta)/2)+2(2"sin"(theta)/2)`
`=3"cos"(theta)/2+4"sin"(theta)/2, theta epsilon[0,pi]`
`F^(')(theta)=-3/2 "sin"(theta)/2+2"cos"(theta)/2`
`F^(')(theta)=0implies"tan"((theta)/2)=4/3`
`:.F(0)=3`
`F(2"tan"^(-1)4/3)=3(3/5)+4(4/5)=5`
`F(pi)=4:.` Range `[3,5]`
Hence possible integer (s) in the range of `F(theta)` in `[0,pi]` are 3