Question

If a,b,c are non-coplanar vectors and `lamda` is a real number, then the vectors `a+2b+3c,lamdab+4c and (2lamda-1)c` are non-coplanar for
A. all value of `lamda`
B. all except one value of `lamda`
C. all except two value of `lamda`
D. no value of `lamda`

Answer 1

Correct Answer - C
The three vectors (a+2b+3c),`(lamdab+4c) annd (2lamda-1)`c are non-coplanar, if
`|(1,2,3),(0,lamda,4),(0,0,2lamda-1)|ne0`
`implies (2lamda-1)(lamda) ne0`
`implies lamda ne0,(1)/(2)`
So, these three vectors are non-coplanar for all except two values of `lamda`.