Question

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

Answer 1

Correct Answer - c
`vecv= lamdaveca + muvecb`
`= lambda( hati +hatj +hatk) + mu(hati - hatj +hatk)`
Projection of `vecv " on " vecc`
`(vecv.vecc)/(|vecc|)= 1/sqrt3`
`or ([(lamda+mu)hati+(lamda-mu)hatj+(lamda+mu)hatk].(hati-hatj-hatk))/sqrt3= 1/sqrt3`
`or lamda + mu - lamda+ mu- lamda- mu =1`
` or mu - lamda =1`
`or lamda = mu -1`
`Rightarrow vecv= (mu-1) (hati+hatj+hatk)+mu(hati-hatj+hatk)`
` = (2mu -1) hati -hati -hatj + (2mu -1) hatk`
At `mu-2 , vecv = 3hati -hatj +3hatk`