`ABCD` is a regular tetrahedron. `M and N` are the mid points of the edges `AB and CD`. It the length of `AB` is a, then `|bar(MN)|^2 =`

ABCD is a regular tetrahedron P & Q are the mid -points of the edges AC and AB respectively, G is the cenroid of the face BCD and theta is the angle between the vectors vec(PG) and vec(DQ) , then

In a regular tetrahedron, if the distance between the mid points of opposite edges is unity, its volume is

In a regular tetrahedron, if the distance between the mid points of opposite edges is unity, its volume is

Point M is the mid point of seg AB. If AB = 8 then find the length of AM.

In the given figure, ABCD is a parallelogram and M, N are the mid-points of AB and CD. The value of theta is