Let `veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk and vecc= hati+hatj-hatk` A vector in the plane of `veca and vecb` whose projections on `vecc` is `1/sqrt3` is

Options

A. `4 hati - hatj + 4hatk`
B. `3hati+hatj - 3hatk`
C. `2hati+hatj- 2hatk`
D. `4hati + hatj -4hatk`

Answer

a

Explanation

A vector in the plane of `veca and vecb` is
`vecu=muveca +lambdavecb= (mu +lamda)hati+ (2mu - lamda) hatj + ( mu +lambda)hatk`
projection of `vecu` on ` vecc = 1/sqrt3`
` Rightarrow (vecu.vecc)/(|vecc|)= 1/sqrt3`
`or vecu.vecc=1`
`or |mu + lambda+ 2mu -lamda-mu-lambda|=1`
`or |2mu -lamda|=1`
`or lamda = 2mu +- 1`
`Rightarrow vecu = 2hati +hatj + 2hatk or 4 hati -hatj + 4hatk` j