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Consider a tetrahedron with faces F(1),F...

Consider a tetrahedron with faces `F_(1),F_(2),F_(3),F_(4)`. Let `vec(V_(1)), vecV_(2),vecV_(3),vecV_(4)` be the vectors whose magnitude are respectively equal to areas of `F_(1).F_(2).F_(3).F_(4)` and whose directions are perpendicular to their faces in outward direction. Then `|vecV_(1) + vecV_(2) + vecV_(3) + vecV_(4)|`, equals:

A

1

B

4

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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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VIBRANT-TEST PAPERS-PART - I : MATHEMATICS
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