Mathematics

Problem

a, b

and

c

are three coplanar vectors. If

a

is not parallel to

b

, show that

c = \frac{\begin{vmatrix} c \cdot a & a \cdot b \\ c \cdot b & b \cdot b \end{vmatrix} a + \begin{vmatrix} a \cdot a & c \cdot a \\ a \cdot b & c \cdot b \end{vmatrix} b}{\begin{vmatrix} a \cdot a & a \cdot b \\ a \cdot b & b \cdot b \end{vmatrix}}