1.

If a=hati+hatj+hatk, b=hati-hatj+2hatk and c=xhati+(x-2)hatj-hatk and if the vector c lies in the plane of vectors a and b, then x equals

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`-2`
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Solution :GIVEN, `a=hati+hatj+hatk, B=hati-hatj+2hatk`
and `c=xhati+(x-2)hatj-hatk`
Since, c lies in the plane of VECTORS a and b, THEREFORE a, b and c are coplanar.
`therefore |(1,1,1),(1,-1,2),(x,(x-2),-1)|=0`
`implies 1(1-2x+4)-1(-1-2x)+1(x-2+x)=0`
`implies 5-2x+1+2x+2x-2=0`
`implies x = - 2 `


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