MTH 101 Study Guide - Final Guide: Parallelepiped, Vector Projection
Document Summary
Spring 2021: answer: for any vectors v1 and v2, (v1 + v2) (v1 v2) = v1 v1 + v2 v1 v1 v2 v2 v2. = (cid:18) x v + y v kvk2 (cid:19) v = (cid:18) x v kvk2 + y v kvk2(cid:19) v. = (cid:18) x v kvk2(cid:19) v +(cid:18) y v kvk2(cid:19) v = projv x + projv y: answer: the key observation is this: the four points lie on the same plane if and only if the. Oc determine a parallelepiped (with a positive volume). Oa, vectors points lie on the same plane if and only if. = 2 + 0 + 3 6= 0. We conclude that the four points do not lie on the same plane. Alternative solution: the plane containing the three points a, b, and c is orthogonal to the vector. = 6i 5j + 3k (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) and hence can be expressed by the equation or.
