Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 13 - Vector Functions - 13.1 Vector Functions and Space Curves - 13.1 Exercises - Page 894: 17


$r(t) =\lt 2+4t, 2t,-2t \gt ; 0 \leq t \leq 1$ $x=2+4t;\\ y= 2t; \\z=-2t ; \\0 \leq t \leq 1$

Work Step by Step

The General vector line equation for the given two points is defined as: $r(t)=(1-t) r_0+t \times r_1$ Now, we have $r(t) =(1-t) \lt 2,0,0 \gt +t \lt 6,2,-2 \gt$ $\implies \lt 2,0,0 \gt - \lt 2t, 0 \times t,0 \times t \gt+\lt 6t ,2t, -2t \gt$ $\implies =\lt 2-2t,0,0 \gt +\lt 6t ,2t, -2t \gt$ Hence, we have $r(t) =\lt 2+4t, 2t,-2t \gt ; 0 \leq t \leq 1$ The parametric equations are as follows: $x=2+4t $ $y= 2t; \\z=-2t$ ;$0 \leq t \leq 1$
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