Find three mutually orthogonal unit vectors in R³ besides ±i, ±j, and ±k. There are multiple ways to do this and an infinite number of answers. For this problem, we choose a first vector u randomly, choose all but one component of a second vector v randomly, and choose the first component of a third vector w randomly. The other components x, y, and z are chosen so that u, v, and w are mutually orthogonal. Then unit vectors are found based on u, v, and w. Start with u = (1,0,2), v= (x,-1,2), and w= V= (1,y,z). The unit vector based on u is . (Type exact answers, using radicals as needed.)

Find three mutually orthogonal unit vectors in R³ besides ±i, ±j, and ±k. There are multiple ways to do this and an infinite number of answers. For this problem, we choose a first vector u randomly, choose all but one component of a second vector v randomly, and choose the first component of a third vector w randomly. The other components x, y, and z are chosen so that u, v, and w are mutually orthogonal. Then unit vectors are found based on u, v, and w. Start with u = (1,0,2), v= (x,-1,2), and w= V= (1,y,z). The unit vector based on u is . (Type exact answers, using radicals as needed.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 48E

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