# A proof of cross product and det

• Jan 27th 2008, 09:13 AM
Prove that $|a \ \times \ b |^2 = det \left(\begin{array}{cc}(a \cdot a)&(a \cdot b)\\(a \cdot b)&(b \cdot b)\end{array}\right)$
So far I have $det \left(\begin{array}{cc}(a \cdot a)&(a \cdot b)\\(a \cdot b)&(b \cdot b)\end{array}\right) = (a \cdot a) \cdot (b \cdot b) - (a \cdot b) \cdot (a \cdot b)$