A parallelepiped `S` has base points `A ,B ,Ca n dD` and upper face points `A^(prime),B^(prime),C^(prime),a n dD '` . The parallelepiped is compressed by upper face `A ' B ' C ' D '` to form a new parallepiped `T` having upper face points `A",B",C"a n dD"` . The volume of parallelepiped `T` is 90 percent of the volume of parallelepiped `Sdot` Prove that the locus of `A"` is a plane.

A parallelepiped S has base points A ,B ,Ca n dD and upper face points A^(prime),B^(prime),C^(prime),a n dD ' . The parallelepiped is compressed by upper face A ' B ' C ' D ' to form a new parallepiped T having upper face points A prime prime,B prime prime,C prime prime and D prime prime . The volume of parallelepiped T is 90 percent of the volume of parallelepiped Sdot Prove that the locus of A" is a plane.

A parallelepiped S has base points A ,B ,Ca n dD and upper face points A^(prime),B^(prime),C^(prime),a n dD ' . The parallelepiped is compressed by upper face A ' B ' C ' D ' to form a new parallepiped T having upper face points A^(prime prime),B^(prime prime),C^(prime prime) and D^(prime prime) . The volume of parallelepiped T is 90 percent of the volume of parallelepiped Sdot Prove that the locus of A^(prime prime) is a plane.

A parallelepiped is formed by planes drawn parallel to coordinate axes through the points A=(1,2,3) and B=(9,8,5). The volume of that parallelepiped is equal to (in cubic units)

A parallelepiped is formed by planes drawn parallel to coordinate axes through the points A=(1,2,3) and B=(9,8,5). The volume of that parallelepiped is equal to (in cubic units)

A parallelepiped is formed by planes drawn parallel to coordinate axes through the points A=(1,2,3) and B=(9,8,5). The volume of that parallelepiped is equal to (in cubic units)

A parallelepiped is formed by planes drawn parallel to coordinate axes through the points A=(1,2,3) and B=(9,8,5). The volume of that parallelepiped is equal to (in cubic units)

Show that a.(b × c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors , a, b and c.

Show that a.(b xx c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors , a, b and c.