Chapter 12 - Vectors and the Geometry of Space - 12.5 Exercises - Page 848: 5

$r=\lt1+t,3t,6+t\gt$ and $x=1+t,y=3t,z=6+t $

Equation of the line is given by $r=r_0+tv$ $r_0=(1,0,6) $ and $v= \lt 1,3,1 \gt$ Thus, the vector equation of the line is $r=(1,0,6) +t \lt 1,3,1 \gt$ $r=\lt1+t,3t,6+t\gt$ Hence, the parametric equations are: $x=1+t,y=3t,z=6+t $