## Proof That Any Vector in Three Dimensions Can Be Written In Terms Of Three Non Collinear, Non Planar Vectors

Theorem

Letbe any three vectors, not coplanar, and no two of which are parallel. Any vector can be written in terms of

Proof

Forsatisfying the conditions of the theorem, write

(1)

Cross multiply this equation on the right byto give

(2)

Take the dot product of (2) byto give

(3)

From (3) then

Similarlyand

Hence