## Thomas' Calculus 13th Edition

Published by Pearson

# Chapter 12: Vectors and the Geometry of Space - Practice Exercises - Page 735: 50

#### Answer

$\dfrac{25}{\sqrt {38}}$

#### Work Step by Step

The formula to determine the distance formula for two vectors $a$ and $b$ is given by: $d=\dfrac{| a \cdot b|}{|b|}$ Thus, we have $a \cdot b=-1(2)+(-1)(3)+(-4)(5)=-25$ and $|a \cdot b|=|-25|=25$ Now, $d=\dfrac{25}{ \sqrt {(2)^2+(3)^2+(5)^2}}=\dfrac{25}{\sqrt {38}}$

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