Answer
$r(t)=(6i-j+9k)+t(i+7j-9k)$, 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 $0\leq t \leq 1$
$r(t)=(1-t)\lt6,-1,9\gt+t\lt7,6,0\gt$
$=\lt6-6t+4t,-1+t+6t,9-9t+0\gt$
$=\lt6+t,-1+7t,9-9t\gt$, for $0\leq t \leq 1$
Hence, $r(t)=(6i-j+9k)+t(i+7j-9k)$, for $0\leq t \leq 1$
