If `veca, vecb, vecc` are non coplanar vectors and `lamda` is a real number, then `[(lamda(veca+vecb), lamda^(2)vecb, lamdavecc)]=[(veca, vecb+vecc,vecb)]` for

Options

A. exactly two values of `lamda`
B. exactly two values of `lamda`
C. no value of `lamda`
D. exacty one value of `lamda`

Answer

C

Explanation

Solution We have
`[(lamda(veca+vecb), lamda^(2)vecb, lamdavecc)]=[(veca, vecb+vecc,vecb)]`
`implieslamda^(4)[(veca+vecb, vecb, vecc)]=[(veca, vecb+vecc, vecb)]`
`implies lamda^(2){[(veca, vecb, vecc)]+[(vecb, vecb, vecc)]}={[(veca, vecb, vecb)]+[(veca, vecc, vecb)]}`
`implies lamda^(2)[(veca, vecb, vecc)]=[(veca, vecb, vecc)]`
`implies(lamda^(2)+1)[(veca, vecb, vecc)]=0`
This is not true for any real value of `lamda` as `[(veca, vecb, vecc)]=0`