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`

Correct Answer – C
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`