University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.5 - Lines and Planes in Space - Exercises - Page 630: 3


$x=5t-2,y=5t, z=3-5t$

Work Step by Step

The parametric equations of a straight line can be found by knowing the value of a vector, such as $v=v_1i+v_2j+v_3k$, passing through a point $P(x_0,y_0,z_0)$ as follows: $x=x_0+t v_1,y=y_0+t v_2; z=z_0+t v_3$ Here, we have $P(-2,0,3)$ and $v=\lt 3-(-2), 5-0,-2-3 \gt =\lt 5,5,-5 \gt$ Thus, we get the parametric equations: $x=5t-2,y=5t, z=3-5t$
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