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Consider tetrahedron with faces F_(1),F_(2),F_(3),F_(4). Let vec(V_(1)),vec(V_(2)),vec(V_(3)),vec(V_(4)), be vectors, whose magnitudes are respectively equal to areas ofF_(1),F_(2),F_(3),F_(4) & whose directions are perpendicular to their faces in outward directon, then |vec(V_(1))+vec(V_(2))+vec(V_(3))+vec(V_(4))|

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Solution :Point on line `C(3+2lambda,1+4lambda,2+5lambda)`
DR's of DC `(2lambda-1,4lambda-2,5lambda-5)`
`DC_|_"line"`
`THEREFORE LAMBDA=(7)/(9)impliesDR's"of"DC ((5)/(9),(10)/(9),(-10)/(9))`
EQUATION of plane : `(5)/(9)(x-3)+(10)/(9)(y-1)-(10)/(9)(z-2)=0`
`therefore` Equation of plane `x+2y-2z=1`


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