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 734: 27


Find ${\bf n}\times{\bf v} $ (or ${\bf v}\times{\bf n} $).

Work Step by Step

The vector ${\bf n}\times{\bf v} $ is perpendicular to both ${\bf n}$ and ${\bf v}$. One condition is obviously satisfied (perpendicular to ${\bf v}$). Being perpendicular to a vector that is perpendicular to the plane, the vector ${\bf n}\times{\bf v} $ lies in a plane parallel to our plane. Thus, the second condition is also satisfied.
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