Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.5 Planes in 3-Space - Exercises - Page 685: 41



Work Step by Step

The parametric equations of the line are given by $$ x=-6t, \quad y=9t, \quad z=36t.$$ Now, substituting in the equation of the plane $$ z=12\Longrightarrow 36t=12\\ \Longrightarrow t=\frac{1}{3}. $$ So the point of intersection is given by $$(-2,3,12).$$
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