If the vectors `a + lamda b + 3c, -2a + 3b - 4c` and `a - 3b + 5c` are coplanar and `a, b, c` are non-coplanar, then the value of `lambda` is

Options

A. 2
B. `-1`
C. 1
D. `-2`

Answer

D

Explanation

Since, the given three vectors are coplanar, therefore one of them shold be expressblle as a llinear Scalars x and y such that
`a+lamda b+3c=x(-2a+3b-4c)+y(a-3b+5c)`
On comparing the coefficient of a, b anc c on both sides, we get
`-2x+y=1, 3x=lamda` and `-4x+5y=3`
On sloving first and third equations, we get
`x=-1/3, y=1/3`
Since, the vectors are coplanar, therefore these values of x and y, also satisty the second equation i.e., `-1-1=lamda`
`:." "lamda=-2`