The lengths of two opposite edges of a tetrahedron are `a` and `b ;` the shortest distane between these edges is `d ,` and the angel between them is `theta` Prove using vectors that the volume of the tetrahedron is `(a b dsi ntheta)/6` .

The lengths of two opposite edges of a tetrahedron of aa n db ; the shortest distane between these edgesis d , and the angel between them if thetadot Prove using vector4s that the volume of the tetrahedron is (a b di s ntheta)/6 .

The length of two opposite edges of a tetrahedron are 12 and 15 units and the shortest distance between them is 10 units. If the volume of the tetrahedron is 200 cubic units, then the angle between the 2 edges is

Given a tetrahedrone D-ABC with AB=12,CD=6. If the shortest distance between the skew lines AB and CD is 8 and angle between them is pi/6 , then find the volume of tetrahedron.

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

If the angel between unit vectors vec aa n d vec b60^0 , then find the value of | vec a- vec b|dot

In a regular tetrahedron, prove that angle theta between any edge and the face not containing that edge is given by cos theta = 1/sqrt3 .

In a regular tetrahedron, let theta be angle between any edge and a face not containing the edge. Then the value of cos^(2)theta is

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

Comprehesion-I Let k be the length of any edge of a regular tetrahedron (all edges are equal in length). The angle between a line and a plane is equal to the complement of the angle between the line and the normal to the plane whereas the angle between two plane is equal to the angle between the normals. Let O be the origin and A,B and C vertices with position vectors veca,vecb and vecc respectively of the regular tetrahedron. The angle between any edge and a face not containing the edge is

Comprehesion-I Let k be the length of any edge of a regular tetrahedron (all edges are equal in length). The angle between a line and a plane is equal to the complement of the angle between the line and the normal to the plane whereas the angle between two plane is equal to the angle between the normals. Let O be the origin and A,B and C vertices with position vectors veca,vecb and vecc respectively of the regular tetrahedron. The angle between any two faces is