MATH 210 Study Guide - Final Guide: Parametric Equation, Cross Product, Horse Length
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Solution: (a) in order to nd an equation for the plane we must know a vector n perpendicular to plane. Using the fact that the cross product of two vectors is perpendicular to each of the vectors, we let n = Qr where p = (1, 0, 3), q = (0, 4, 2), and r = (1, 1, 1). N = h 1, 4, 1i h1, 3, 1i , N = (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) 1 3 1 (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) N = [(4)( 1) ( 1)( 3)] [( 1)( 1) ( 1)(1)] + k[( 1)( 3) (4)(1)], Using p = (1, 0, 3) as a point on the plane we have. 7(x 1) 2y (z 3) = 0 (b) let s = (x, y, z) be the point on the plane closest to the point (1, 0, 1). The line that connects (x, y, z) and (1, 0, 1) is perpendicular to the plane.
