Answer
$\lt2+2t,-1+7t,4-3t\gt$, 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 $0\leq t \leq 1$
$r(t)=(1-t)\lt2,-1,4\gt+t\lt4,6,1\gt$
$=\lt2-2t+4t,-1+t+6t,4-4t+t\gt$
$=\lt2+2t,-1+7t,4-3t\gt$, for $0\leq t \leq 1$
