Let `veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj - hatk` be three vectors. A vectors `vecv` in the plane of `veca and vecb` , whose projection on `vecc is 1/sqrt3` is given by

Options

A. `hati-3hatj+3hatk`
B. `-3hati-3hatj-hatk`
C. `3hati-hatj+3hatk`
D. `hati+3hatj-3hatk`

Answer

C

Explanation

Let `V=a+ lamda b`
`v=(1+lamda )hati +(1-lamda ) hatj +(1+lamda )hatk`
projection of v on c`=(v.c)/(|c|)=(1)/(sqrt(3))`
`implies ((1+lamda )-(1-lamda )-(1+lamda ))/(sqrt(3))=(1)/(sqrt(3))`
`implies lamda =2`
`therefore v= 3 hati - hatj + 3 hatk`