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 - Section 12.5 - Lines and Planes in Space - Exercises 12.5 - Page 727: 37


$\dfrac{9 \sqrt {42}}{7}$

Work Step by Step

The distance formula for two vectors can be calculated as: $d=\dfrac{|p \times q|}{|q|}$ Thus, we have $p \times q=\lt 30,6,6\gt $ and $|p \times q|=\sqrt{(30)^2+(6)^2+(6)^2}=\sqrt{900+36+36}=18 \sqrt {3}$ Thus, $d=\dfrac{18 \sqrt {3}}{ \sqrt {14}}=\dfrac{9 \sqrt {42}}{7}$
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