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: 29


$\dfrac{\sqrt {78}}{3}$

Work Step by Step

The distance formula for two vectors $p$ and $q$ can be calculated as: $d=\dfrac{|p \times q|}{|p|}$ Thus, we have: $p \times q=\lt -1,3,-4 \gt$ and $|p \times q|=\sqrt{(-1)^2+(3)^2+(-4)^2}=\sqrt {26}$ Thus, $d=\dfrac{\sqrt {26}}{\sqrt{(-1)^2+(1)^2+(1)^2}}=\dfrac{\sqrt {26}}{ \sqrt {3}}=\dfrac{\sqrt {78}}{3}$
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