Prove that the shortest distance between the diagonals of a rectangular parallelopiped whose coterminous sides are a, b, c and the edges not meeting it are

The volume of a parallelopiped whose coterminous edges are 2veca , 2vecb , 2 vec c , is

The shortest distance between a diagonal of a unit cube and the edge skew to it, is

The shortest distance between a diagonal of a unit cube and the edge skew to it, is

The shortest distance between a diagonal of a unit cube and the edge skew to it,is

Prove that the S.D. between a diagonal of a rectangular parallelopiped and its edges not meeting it are: (bc)/(sqrt(b^2+c^2)),(ca)/(sqrt(c^2+a^2)), (ab)/(sqrt(a^2+b^2)) where a,b,c are lengths of the edges.

The shortest distance between a diagonal of a cube, of edge-length one unit and the edge not meeting it, is

If (2, 5, 1) and (9, 10, 5) are the ends of a diagonal of a rectangular parallelopiped whose faces are parallel to the coordinate planes, then the lengths of edges are

Show that tha angles between the diagonals of a rectangular parallelopiped having sides a,b and c are cos^(-1)((|alpha|)/(a^(2)+b^(2)+c^(2))) , where alpha=pma^(2)pmb^(2)pmc^(2)and|alpha|!=a^(2)+b^(2)+c^(2) . Hence find the angle between the diagonals of a cube.