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 871: 17


$r(t)=(6i-j+9k)+t(i+7j-9k)$, for $0\leq t \leq 1$

Work Step by Step

The vector equation of a line segment from $r_0$ to $r_1$ is: $r(t)=(1-t)r_0+tr_1$, for $0\leq t \leq 1$ $r(t)=(1-t)\lt6,-1,9\gt+t\lt7,6,0\gt$ $=\lt6-6t+4t,-1+t+6t,9-9t+0\gt$ $=\lt6+t,-1+7t,9-9t\gt$, for $0\leq t \leq 1$ Hence, $r(t)=(6i-j+9k)+t(i+7j-9k)$, for $0\leq t \leq 1$
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