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: 52


$$ x=3+3t, \quad y=-1+5t, \quad 1-7t.$$

Work Step by Step

The normal vector to the plane is $$ n=\langle3,5,-7 \rangle $$ and it is easy to notice that the normal vector to the plane is the dirction vector of the line and hence the equation of the line is $$ r(t)=\langle3,-1,1 \rangle+t\langle3,5,-7 \rangle.$$ Hence the parametric equations of the line are $$ x=3+3t, \quad y=-1+5t, \quad 1-7t.$$
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