Let be unit vectors. By using suffix notation, prove that
The three distinct points with position vectors lie on the surface of the unit sphere centred on the origin . The spherical distance between the points and , denoted , is the length of the (shorter) arc of the circle with centre passing through and . Show that
A spherical triangle with vertices is a region on the sphere bounded by the three circular arcs . The interior angles of a spherical triangle at the vertices are denoted , respectively.
By considering the normals to the planes and , or otherwise, show that
Using identities (1) and (2), prove that
For an equilateral spherical triangle show that .