Answer
See below.
Work Step by Step
Let $u=(a,b,c)$.
We know that for a matrix
$
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
$
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
$u×u$ is the determinant of the matrix $\begin{bmatrix}
i& j & k \\
a& b&c\\
a&b &c \\
\end{bmatrix}
$
Thus $u×0=(b\cdot c-c\cdot b,c\cdot a-a\cdot c,a\cdot b-b\cdot a)=(0,0,0).$
Thus we proved what we had to.
