Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 666: 30


$$\langle 2,0,1 \rangle.$$ (Other solutions are possible.)

Work Step by Step

Assume that the vector is $\langle a, b,c \rangle $, since the vectors are orthogonal, then we have $$\langle a,b,c \rangle \cdot \langle-1,2,2\rangle=0\Longrightarrow -a+2b+2c=0.$$ We can pick any vector $\langle a,b,c \rangle$ that satisfies the above equation. Hence, we can choose the vector as follows $$ a=2, b=0, c=1$$ That is the vector is given by $$\langle 2,0,1 \rangle.$$ (Many other vectors are possible.)
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