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,prove that angle theta between any edge and the face not containing that edge is given by cos theta=(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 angle 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

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

The angle between one of the diagonals of a cube and one of its edge is theta then sqrt(3)cos theta=

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

The lengths of two opposite edges of a tetrahedron of a and b; the shortest distane between these edgesis d, and the angel between them if theta. Prove using vector 4 that the volume of the tetrahedron is (abdisn theta)/(6)

If volume of a regular tetrahedron of edge length k is V and shortest distance between any pair of opposite edges of same regular tetrahedron is d,then find the value of (d^(3))/(V)