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If veca and vecb are any two unit vector...

If `veca and vecb` are any two unit vectors, then find the greatest postive integer in the range of `(3|veca + vecb|)/2+2|veca-vecb|`

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
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
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