You have points A(-1,3,2) B(-1,5,2) C(1,5,-2) .. Prove that triangle ABC is a right triangle.
We know dot product and cross product and all the minor stuff that you need to do those, but cross product is the most advanced stuff we know. Mind you, I don't think we need cross product for this (in my opinion anyways). The way I can think of doing it is proving that AB(dot)AC or CA(dot)CB or BA(dot)BC equals zero... If it is zero, those vectors are 90 degrees, and ABC is a right triangle. But this is a lot of work! I don't mind doing it, but I have a feeling there is an easier way.
Anyone have any ideas?