1.

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

Answer»

2
`-1`
1
`-2`

Solution :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`


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