1. The problem statement, all variables and given/known data Show that vector C = (BA + AB) / (A + B) is an angle bisector of A and B. Where vectors are represented by bold font, and magnitudes are regular font. 2. Relevant equations A ⋅ C = A C cos(θ) ⇒ cos(θ) = (A ⋅ C) / (A C) B ⋅ C = B C cos(θ) ⇒ cos(θ) = (B ⋅ C) / (B C) 3. The attempt at a solution We know that if C is a bisector of A and B, then ∠AC =∠BC = θ must be true. I set the above equations equal to each other to get; (A ⋅ C) / (A C) = (B ⋅ C) / (B C) I notice the magnitude C cancels and then cross multiply the expression to get; (A ⋅ C)B = (B ⋅ C)A I bring the right side over and use identities of dot products to get; C ⋅ [BA - AB] = 0 This is where I am stuck I don't know how to take it any further. I would appreciate a push in the right direction.