1. The problem statement, all variables and given/known data The point P and Q have postion vectors a + b, and 3a - 2b respectively, relative to the origin O.Given that OPQR is a parallelogram express the vector PQ and PR in terms of a and b. By evaluating two scalar products show that if OPQR is a square then |a |2 = 2 |b |2 3. The attempt at a solution OP = a + b OQ = 3a -2b PQ = OR= PO + OQ = -OP +OQ = -(a + b) + (3a - 2b) = 2a - 3b PR = PO + OR = -OP + OR = -(a + b) + (2a - 3b) = a - 4b So now the question says use two scalar products to show |a |2 = 2 |b |2. I'm assuming since the question ask for these two vectors in terms of a, and b that you will have to utilize it to get the result. So I drew out the square for a visualization. So since its a square it means the dot product of OP.PQ= 0 (a + b)(2a - 3b) = 2a2 -ab -3b2 = 0 ab = 2a2 -3b2 PR.OQ= 0 (Since their perpendicular) (a-4b)(3a - 2b) =0 3a2 - 14ab +8b2=0 3a2 -14(2a2 -3b2) +8b2=0 3a2 -28b2 +42a2 + 8b2=0 -25a2+50b2=0 25a2=50b2 a2= 2b2 Is their a faster way to work it or is this correct ? ????