MHB How do I Find the Vector Coordinates to Solve for Trihedral Angle?

[Julian1]

Hi everyone,

Here's the problem I have.

Given two unit vectors A, B and angle φ between them. Find the coordinates (in 3D) of a unit vector C so that the angles between C and A,B be α and β respectively.
α + β => φ and α + β + φ <= 360°

It looks trivial to me and yet here I am asking for help:)

I have two equations from the dot products:
A.C = cos(α)
B.C = cos(β)
and I need a third one to solve the problem?

Thanks!Julian.

 

[Julian1]

Re: find the vector coordinates

I have found the solution.

The third equation is the triple product.

A.BxC = V

where

V² = 1 + 2*cos(α)*cos(β)*cos(φ) – cos²(α) – cos²(β) – cos²(φ)

Trihedral Angle | OPEN MIND