Prove that the smaller angle between any two diagonals of a cube is `cos^(-1)""(1)/(3)`.

Find the angle between any two diagonals of a cube.

The angle between any two orthogonal unit vectors

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)) .

An ellipse is inscribed in a reactangle and the angle between the diagonals of the reactangle is tan^(-1)(2sqrt(2)) , then find the ecentricity of the ellipse

If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4vecb are perpendicular to each other then the angle between veca and vecb is (A) 45^0 (B) 60^0 (C) cos^-1(1/3) (D) cos^-1(2/7)

If vec aa n d vec b are any two vectors of magnitudes 1 and 2, respectively, and (1-3 vec adot vec b)^2+|2 vec a+ vec b+3( vec axx vec b)|^2=47 , then the angel between vec aa n d vec b is a. pi//3 b. pi-cos^(-1)(1//4) c. (2pi)/3 d. cos^(-1)(1//4)

Prove that: cos^2 theta (1 + tan^2 theta) = 1

A line makes angles alpha,beta,gammaa n ddelta with the diagonals of a cube. Show that cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4//3.

When the light ray is incident normal to the interface between any two media, the angle of incidence is ___________ .