Given there are two vectors $w,v$ with $||w||=4$ , $||v||=1$ and $\phi=\frac{2\pi}{3}$
How do you transform the following expression into a form in which it can be computed with the given information?
$$ < w \times 5v,v-3w> $$
The cross product as first factor is what puzzles me about this
You should know that the dot product is distributive. $\left<\mathbf{a}, \mathbf{b} + \mathbf{c} \right> = \left<\mathbf{a}, \mathbf{b} \right> + \left<\mathbf{a}, \mathbf{c} \right>$
So you should be able to obtain two dot products from this expression. Each of them would be what is called "scalar triple products."
How is the result of any cross product oriented with respect to the original vectors?
It might also help to be informed that scalars can be taken outside dot and cross products.
$\left<g\mathbf{a}, \mathbf{b} \right> = \left<\mathbf{a}, g\mathbf{b} \right> = g\left<\mathbf{a}, \mathbf{b} \right> $
$(g\mathbf{a}) \times \mathbf{b} = \mathbf{a} \times (g\mathbf{b}) = g(\mathbf{a} \times \mathbf{b} )$