Answer
$${\bf{r}}(t)
= \langle 1+2t,2+t,-8+3t \rangle.$$
Work Step by Step
A vector parametrization for the given line is given by
$${\bf{r}}(t)= \langle 1,2,-8 \rangle +t \langle 2,1,3 \rangle\\
= \langle 1+2t,2+t,-8+3t \rangle.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 13 - Vector Geometry - 13.2 Vectors in Three Dimensions - Exercises - Page 659: 33
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