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: 15

Answer

$\left\{\begin{array}{l} x=1\\ y=t\\ z=0 \end{array}\right., \quad 0\leq t \leq 1$

Work Step by Step

Given a point on the line $P(x_{0},y_{0},z_{0})$ and if the line is parallel to ${\bf v}=\langle v_{1},v_{2},v_{3}\rangle$, the standard parametrization is given by formula (6), $\left\{\begin{array}{l} x=x_{0}+v_{1}t\\ y=y_{0}+v_{2}t\\ z=z_{0}+v_{3}t \end{array}\right., \quad -\infty \lt t \lt \infty$ --- $\overrightarrow{PQ}=\langle 1-1,1-0, 0-0 \rangle=\langle 0,1,0\rangle= {\bf v}$. A point on the line is $P(1,0,0)$, so a parametrization can be $\left\{\begin{array}{l} x=1\\ y=0+t\\ z=0 \end{array}\right., \quad -\infty \lt t \lt \infty$ when $t=0$, the point defined is $(1,0,0)$ when $t=1$, the point defined is $(1,1,0)$ so, the line segemnt is parametrized with $\left\{\begin{array}{l} x=1\\ y=t\\ z=0 \end{array}\right., \quad 0\leq t \leq 1$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.