Economics 1021A/B Study Guide - Quiz Guide: Unit Vector, Parallelogram, Cross Product

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ECON 1021A/B Full Course Notes
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ECON 1021A/B Full Course Notes
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We know that vectors u and v are perpendicular (i. e. orthogonal) if and only if u v = 0. For u = (4, 1, k) and v = (5, 1, 3), we get u v = (4, 1, k) (5, 1, 3) = (4)(5)+(1)(1)+(k)( 3) = 20+1+( 3k) = 21 3k. Therefore we need 21 3k = 0, which means we must have. We know that two vectors u and v are parallel if and only if one is a scalar multiple of the other. Therefore it must be true that v = cu for some value of the scalar c. we see that cu = c(2, 6, k) = (2c, 6c, ck) Therefore we must have v = (2c, 6c, ck) for some values c and k. since v = ( 1, 3, 2), we need ( 1, 3, 2) = (2c, 6c, ck). From the rst component, we see that we must have c = 1.

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