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: 12

Answer

$x=0,y=0, z=t$

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 the vector $v=\lt 0,0,1 \gt$ and $P=(0,0,0)$; the point P lies on the z-axis. Thus, we get the parametric equations: $x=0+0t,y=0+0t, z=0+1t$ Hence, $x=0,y=0, z=t$
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