Mathematics

Problem

For any three vectors

a, b

and

c

prove

\text{that } [a b c]^2 = \begin{vmatrix} a \cdot a & a \cdot b & a \cdot c \\ b \cdot a & b \cdot b & b \cdot c \\ c \cdot a & c \cdot b & c \cdot c \end{vmatrix}