Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 5 - Inner Product Spaces - 5.5 Chapter Review - Additional Problems - Page 377: 12

Answer

$d=\frac{6}{\sqrt 14}$

Work Step by Step

Using the formula from Exercise 28, the distance of a point $P(x_0,y_0,z_0)$ to the plane $P..ax+by+cz+d=0$ is given by: $$d(P,P)=\frac{|x_0.a+y_0.b+z_0.c+d|}{\sqrt a^2+b^2+c^2} \\ =\frac{0.2+0.(-1)+0.3+(-6)}{\sqrt 2^2+(-1)^2+3^2}\\ = \frac{|-6|}{\sqrt 4+1+9}\\ =\frac{6}{\sqrt 14}$$ Hence, $d=\frac{6}{\sqrt 14}$
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