QJEEAdv04Ma5771: JEE Advanced 2004 Mathematics - Class 12 JEEAdv04Ma5771 Solution: A parallelopiped ′ S ′ has base points A , B , C and D and…

A parallelopiped $${}^{\prime }{S}^{\prime }$$ has base points $$A,B,C$$ and $$D$$ and upper face points $$A^{\prime },$$ $$B^{\prime },$$ $$C^{\prime }$$ and $$D^{\prime }.$$ This parallelopiped is compressed by upper face $$A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$$ to form a new parallelopiped $${}^{\prime }{T}^{\prime }$$ having upper face points $$A^{″},B^{″},C^{″}$$ and $$D^{″}.$$ Volume of parallelopiped $$T$$ is $$90$$ percent of the volume of parallelopiped $$S.$$ Prove that the locus of $${}^{\prime }{A}^{‴},$$ is a plane.