1. The problem statement, all variables and given/known data You have a diameter in a circle, 2R. Show that the angle drawn from the end points of the diameter to the circle is 90 by Linear Algebra. 3. The attempt at a solution The situation seems to be E^3. We get triangle A and B inside the circle such that we have ABCD which has two 90 angles: ABC and ADC. Let one axis be along AB, one axis along AD and one axis along AC such that A = (0,0,0), B = (1,0,0), C = (0,0,1) and D = (0,1,0). We want to show that the dot product between AB and BC is zero AND the product between AD and DC is zero. #1: CB = (-1,0,1) OB = (-1,0,0) CB * OB = 1 which is a contradiction to the wanted result. This would mean that the angle is not 90 which is however false.