If `veca, vecb, vecc` are non coplanar vectors and `lamda` is a real number, then the vectors `veca+2vecb+3vecc, lamdavecb+4vec` and `(2lamda-1)vecc` are non coplanar for

Options

A. no value of `lamda`
B. all except one value of `lamda`
C. all except two values of `lamda`
D. all values of `lamda`

Answer

C

Explanation

Let `vec(alpha)=veca+2vecb+3vecc, vecbeta=lamdavecb+4vecc` and `vecgamma=(2lamda-1)vecc`.
Then
`[vecalpha vecbeta vecgamma]=|(1,2,3),(0,lamda,4),(0,0,(2lamda-1))|[veca vecb vecc]`
`implies[vec(alpha) vec(beta) vec(gamma]=lamda(2lamda-1)[veca vecb vecc]`
`implies[alpha vec(beta) vec(gamma)]=0` if `lamda=0,1/2[ :' [veca vecb vecc]!=0]`
Hence `vec(alpha), vec(beta),vec(gamma)` are non coplanar for all values of `lamda` except two values `0` and `1/2`.