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 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)

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

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)

The shortest distance between any two opposite edges of a tetrahedron formed by the planes y+z=0, x+z=0, x+y=0 and x+y+z=sqrt(6) 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

The shortest distance between any two opposite edges of a tetrahedron formed by the planes y+z=0 , x+z=0 , x+y=0 and x+y+z=sqrt(6) is

If hata and hatb are two unit vectors and theta is the angle between them then vector 2hatb+hata is a unit vector if (A) theta= pi/3 (B) theta=pi/6 (C) theta=pi/2 (D) theta=pi

The shortest distance between any two opposite edges of the tetrahedron formed by planes x+y=0, y+z=0, z+x=0, x+y+z=a is constant, equal to