For vectors a and b , prove that

Question

For vectors \(\vec{a}\)and \(\vec{b}\), prove that |\(\vec{a}\) x \(\vec{b}\)|² =  \(\begin{vmatrix} \vec{a}.\vec{a} &\vec{a}.\vec{b} \\[0.3em] \vec{a}.\vec{b}& \vec{b}.\vec{b} \end{vmatrix}\)

Answer 1

Let θ be the angle between vectors \(\vec{a}\) and \(\vec{b}\)