1. The problem statement, all variables and given/known data By considering A x (B x A) resolve vector B into a component parallel to a given vector A and a component perpendicular to a given vector A. 2. Relevant equations a x (b x c) = b (a ⋅ c) - c (a ⋅ b) 3. The attempt at a solution I've applied the triple product expansion and reached A x (B x A) = B (A ⋅ A) - A (A ⋅ B) = |A|2 B - |A||B|cos(θ) A and hit a brick wall. I'm not entirely sure what the question is asking me to do, and I feel like I'm missing crucial information. Should I be splitting vectors A and B into their cartesian components? EDIT: I got it. Taking A x (B x A) = |A|2 B - A (A ⋅ B) , I can rearrange to find |A|2 B = A x (B x A) + A (A ⋅ B) Dividing through by |A|2 results in B = A x (B x A) |A|-2 + A ((A ⋅ B)/|A|2) So B is given as a component perpendicular (first term) and parallel (second term) to A. I'm fairly sure this is right anyway. Stupid I suddenly work this out after posting here after looking at it for 30 mins before!