Answer to Question #115682 in Analytic Geometry for Sire

Question

Suppose u; v and w are vectors in 3 space, where u = (u1;u2; u3) ; v = (v1; v2; v3) and w = (w1;w2;w3) :
Express (u x v) x w as a determinant

Answer 1

$(\vec{u}*\vec{v})*\vec{w}=(\vec{w}.\vec{u})\vec{v}-(\vec{w}.\vec{v})\vec{u}$

$=\begin{vmatrix} (\vec{w}.\vec{u})& (\vec{w}.\vec{v})\\ \vec{u} & \vec{v} \end{vmatrix}$