Resolving Vectors Using the Vector Triple Product

[BobJimbo]

The problem:
By considering w x (p x w) resolve vector p into a component parallel to a given vector w and a component perpendicular to a given vector w.

Hint: a x (b x c) = b(a x c) - c(a x b)

I'm afraid I really have no idea where to go with this one. The hint leads to: p(w.w) - w(w.p) = |w^2|p - |w||p|cosΘ w

 

[Fightfish]

Hint 1: How is the term $|w|^2 \vec{p}$ related to the vector $\vec{p}$?
Hint 2: How is $\vec{w}\times (\vec{p} \times \vec{w})$ related to the vector $\vec{w}$? For instance, is it parallel or it is perpendicular to $\vec{w}$?

 

[BobJimbo]

Agh, so simple. Thanks! (For the solution and for how to write vectors)