1.

If the vectors vec(a)+lambdavec(b)+3vec(c), -2vec(a)+3vec(b)-4vec(c) and vec(a)-3vec(b)+5vec(c) 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 should be expressible as a linear EQUATION of the remaining two ie, there exist two scalers x and y such that
`vec(a)+LAMBDA vec(b)+3vec(c)=x(-2vec(a)+3vec(b)-4vec(c))+y(vec(a)-3vec(b)+5vec(c))`
On campairing the coefficient of `vec(a), vec(b) and vec(c)` on both sides, we get `-2x+y=1,3x-3y=lambda`
and `-4x+5y=3`
On solving first adnd third equations, we get
`x=-(1)/(3),y=(1)/(3)`
Solving, the vectors are coplanar, therfore tehee values of x and y, also satisfy the second equation i.e. `-1,-1=lambda`
`therefore lambda=-2`


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