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

Let k be the length of any edge of a regular tetrahedron (a tetrahedron whose edges are equal in length is called a regular tetrahedron). Show that the angel between any edge and a face not containing the edge is cos^(-1)(1//sqrt(3)) .

Let k be the length of any edge of a regular tetrahedron (a tetrahedron whose edges are equal in length is called a regular tetrahedron). Show that the angel between any edge and a face not containing the edge is cos^(-1)(1//sqrt(3)) .

find the height of the regular pyramid with each edge measuring l cm. Also, (i) if alpha is angle between any edge and face not containing that edge, then prove that cosalpha=1/sqrt3 (ii) if beta is the between the two faces, then prove that cosbeta=1/3

Prove that : sec theta + cos theta != 3/2

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

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

Solve : sqrt3 sin theta - cos theta = sqrt2.

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 .

If veca=(3,1) and vecb=(1,2) represent the sides of a parallelogram then the angle theta between the diagonals of the paralelogram is given by (A) theta=cos^-1(1/sqrt(5)) (B) theta=cos^-1(2/sqrt(5)) (C) theta=cos^-1 (1/(2sqrt(5))) (D) theta = pi/2