Answer
See the explanation below.
Work Step by Step
The three vectors in component form can be expressed as:
$u =\lt u_{1}, u_{2}, u_{3}\gt $ and $v =\lt v_{1}, v_{2}, v_{3}\gt $ and $w =\lt w_{1}, w_{2}, w_{3}\gt $
Their scalar triple vector can be determined as:
$u \cdot (v \times w)=\begin{vmatrix}u_1&u_2& u_3 \\v_1&v_2&v_3\\w_1&w_2& w_3 \end{vmatrix}$
Significance: This scalar triple vector yields the volume of the parallelopiped formed by the three vectors $\vec{u}$, $\vec{v}$ and $\vec{w}$
