MAT223H1 Study Guide - Quiz Guide: Orthogonal Complement, Row And Column Spaces, Novella
Document Summary
November 24, 2011: anghel, s. arkhipov, s. shahroki-tehrani, s. uppal. 1 of 7: consider the points p = (1, 2, 3) and q = (4, 5, 6) in r3. [6] (a) find an equation for the plane that passes through the origin and contains the points. Express your answer in the form ax + by + cz = d. If the normal vector to the plane is n = (a, b, c), then n p = 0 and n q = 0 which gives the system a + 2b + 3c = 0. Solving this system gives n span{(1, 2, 1)}. Therefore the equation of the plane is x 2y + z = k for some constant k. since the plane passes through (0, 0, 0) we must have k = 0. Scaling by -3, we get that the equation of the plane is x 2y + z = 0.
