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*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)

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