MATH 210 Study Guide - Final Guide: Dot Product, Cross Product, Parallelogram
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Solution: (a) the vectors p q and p r are obtained by subtracting coordinates as follows: P q = h1 ( 1), 2 4, 9 1i = h2, 2, 8i. P r = h5 ( 1), 10 4, 1 1i = h6, 6, 0i. The lengths of sides p q and p r are the magnitudes of the above vectors: P r(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12) (b) use the dot product to determine the angle: cos = cos = || p q|||| p r|| (2)(6) + ( 2)(6) + (8)(0) (6 2)(6 2) cos = 0. 1 (c) a vector perpendicular to the plane is the cross product of p q and p r which both lie in the plane. N = [( 2)(0) (8)(6)] [(2)(0) (8)(6)] + k [(2)(6) ( 2)(6)] N = 48 + 48 + 24 k. Using p = ( 1, 4, 1) as a point on the plane, we have:
