Let a,b,c be real numbers with `a^2 + b^2 + c^2 =1`. Show that the equation `|[ax-by-c,bx+ay,cx+a],[bx+ay,-ax+by-c,cy+b],[cx+a,cy+b,-ax-by+c]|=0` represents a straight line.

Explanation

To show that the determinant

\[
D = \begin{vmatrix}
ax - by - c & bx + ay & cx + a \\
bx + ay & -ax + by - c & cy + b \\
cx + a & cy + b & -ax - by + c
\end{vmatrix} = 0
...