Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises - Page 853: 27


$a=\frac{(i-j-k)}{\sqrt 3}$

Work Step by Step

$a=xi+yj+zk$ Since unit vector $a$ is orthogonal to both$ i+j$ and $i+k$ then the product equals zero in both cases. $x \cdot 1+y \cdot 1=0$ $x \cdot 1+z \cdot 1=0$ From these inequalities, we get $x=-y$ and $x=-z$ Thus, $a=xi-xj-xk$ Since $a$ is a unit vector and $|a|=\sqrt {3x^2}=1$ Thus, $x=\frac{1}{\sqrt 3}$ $a=\frac{1}{\sqrt 3}(i-j-k)$ Hence, $a=\frac{(i-j-k)}{\sqrt 3}$
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