Calculus 8th Edition

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

Chapter 12 - Vectors and the Geometry of Space - 12.5 Equations of Lines and Planes - 12.5 Exercises - Page 872: 37



Work Step by Step

The line of intersection is given as: $a=u \times v$ where $u=\lt1,2,3\gt$ and $v=\lt2,-1,1\gt$ Thus, $a=u \times v=\lt5,5,-5\gt$ and $b=\lt3,-1,5\gt$ Now, $n=a\times b=\lt20,-40,-20\gt$ The general form of the equation of the plane is: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$ or, $ax+by+cz=ax_0+by_0+cz_0$ Plugging in the values $\lt20,-40,-20\gt$, we get $20(x-3)-40(y-1)-20(z-4)=0$ After simplification, we get $x-2y-z=-3$
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