Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.6 Parametric Surfaces and Their Areas - 16.6 Exercises - Page 1160: 19



Work Step by Step

The vector equation of a plane containing the vectors $b_{1}$ and $b_{2}$ and containing a point with position vector $a$ is $r(u,v)=a+ub_{1}+vb_{2}$ The plane through the origin that contains the vectors $i- j$ and $j-k$ and the plane contains the origin, whose position vector is $0i+0j+0k$ Therefore, the vector equation of the plane is $r(u,v)=(0i+0j+0k)+u(i-j+0k)+v(0i+j-k)$ $r(u,v)=(0+u+0)i+(0-u+v)j+(0+0-v)k$ This implies $r(u,v)=ui+(v-u)j-vk$ Hence, the parametric representation of the plane is $x=u,y=v-u,z=-v$
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