91Ó°ÊÓ

If \(u=(1,2,2)\) and \(v=(-6,2,3)\), find the component of \(u\) in the direction of \(\boldsymbol{v}\) and the component of \(v\) in the direction of \(\boldsymbol{u}\).

Use vector methods to show that the diagonals of a rhombus are perpendicular.

Using vector methods, prove the sine rule, $$ \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} $$ and the cosine rule, $$ c^{2}=a^{2}+b^{2}-2 a b \cos C $$

$$ \text { Sketch the scalar field } T(x, y)=x^{2}-y \text {. } $$