T is a parallelopipe in which A, B, C ,and D are the vertices of one face. And the face just above it has corresponding vertices A`, B`, C`, D`. T is now compressed to S with face ABCD remaining same and A`, B`, C`, D` shifted to A", B", C", D" in S.
The volume of parallelopiped S is reduced to 90% o fT.
Prove that locus of A" is a plane!
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1 Answers
1let the equation of the plane ABCD be ax+by+cz+d=0
the point A" be (alpha,beta,gamma) and the height of the parallelopiped be h
then |a(alpha)+b(beta)+c(gamma)+d|/√a2+b2+c2=90%h
a(alpha)+b(beta)+c(gamma)+d=+/- 0.9h√a2+b2+c2
thus locus is ax+by+cz+d=+/-0.9h√a2+b2+c2
thus locus of A" is a plane parallel to plane ABCD