1. The problem statement, all variables and given/known data Given position vectors: OA ( i + 2j - k) ; OB ( -i + 2j +3k); OC ( 2i + j + 4k) Given that OA is perpendicular to OB. The Question : Show that OA is normal to the plane OBC. 2. Relevant equations r . n = d To find the normal of the plane OBC, I used n = BO x BC d = OB . n 3. The attempt at a solution Equation of plane OBC: BO = -OB = i - 2j - 3k BC = OC - OB = (2,1,4) - (-1,2,3) = (3,-1,1) n = BO x BC = (5,10,-5) d = OB . n = (-1,2,3) . (5,10,-5) = 0 ∴ Equation of plane OBC = r. (5,10,-5) = 0 How do I show that OA is normal to the plane? I know that it is related to the statement - 'OA is perpendicular to OB'. However, I do not know how can it be applied into the question. I hope someone can help me out. Thank you for your time!