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: 20


$r(t) =\lt a+t(u-a),b+t(v-b),c+t(w-c) \gt$; $x=a+t(u-a)$ and $y= b+t(v-b)$ and $z=c+t(w-c)$ and $0 \leq t \leq 1$

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 $r(t)=(1-t) \times \lt a,b,c \gt +t \times \lt u,v,w \gt$ $\implies \lt a-at,b-bt, c-ct \gt + \lt ut,vt,wt\gt$ $\implies \lt a+t(u-a),b+t(v-b),c+t(w-c) \gt$ Answer: $r(t) =\lt a+t(u-a),b+t(v-b),c+t(w-c) \gt$ Hence, the parametric equations are as follows: $x=a+t(u-a)$ and $y= b+t(v-b)$ and $z=c+t(w-c)$ and $0 \leq t \leq 1$
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