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 egge is `cos^(-1)(1//sqrt3)`

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)) .

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

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 .

If K is the length of any edge of a regular tetrahedron, then the distance of any vertex from the opposite face 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 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

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 value of [vecavecbvecc]^(2) is

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

Four point masses each of mass m are placed on vertices of a regular tetrahedron. Distance between any two masses is r .