A parallelepiped S has base points A, B, C and D and upper face points `A', B', C' and D'`. The parallelepiped is compressed by upper face `A'B'C'D'` to form a new parallelepiped T having upper face points `A'', B'', C'' and D''`. The volume of parallelepiped T is 90 percent of the volume of parallelepiped S. 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",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 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 through the points P(6,8,10)a n d(3,4,8) parallel to the coordinate planes. Find the length of edges and diagonal of the parallelepiped.

A parallelepiped is formed by planes drawn through the points P(6,8,10)a n d(3,4,8) parallel to the coordinate planes. Find the length of edges and diagonal of the parallelepiped.

Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ad = bc.

If the points A(-2,-1),B(1,0),C(a,3) and D(1,b) form a parallelogram ABCD, Then the values of a and b are

A parallelepiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate lanes. The length of a diagonal of the parallelepiped is a. 7 b. sqrt(38) c. sqrt(155) d. none of these

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=11 hat i ,\ vec b=2 hat j ,\ vec c=13 hat k .

In A B C ,\ D and E are the mid-points of A B and A C respectively. Find the ratio of the areas of A D E and A B C .