Answer
$x(t)=10-5t,y(t)=3+3t,z(t)=1-4t$, 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 $0\leq t \leq 1$
$r(t)=(1-t)\lt10,3,1\gt+t\lt5,6,-3\gt$
Hence, the parametric equations are:
$x(t)=10-5t,y(t)=3+3t,z(t)=1-4t$, for $0\leq t \leq 1$
