Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Practice Exercises - Page 735: 47


The vector is parallel to the plane.

Work Step by Step

Apply orthogonality test. This implies $n \cdot v=\lt 2,1,0 \gt \cdot \lt 2,-4,1 \gt$ or, $n \cdot v=2(2)+1(-4)+0(1)=0$ This means that the vector $v$ is orthogonal to the normal plane's normal vector $n$. Therefore, the vector is parallel to the plane.
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