Answer
$(7,-4,3)$
Work Step by Step
Vector equation of a line joining the points with position vectors $r_0$ and $r_1$ is:
$r=r_0+tv$
Put $r_0=\lt 1,0,1\gt$ and $r_1= \lt 3,-2,1\gt $
$r=\lt 1+3t,-2t,1+t\gt$
Parametric equations of the line are:
$x= 1+3t,y=-2t,z=1+t$
As we are given the equation of the plane is:
$x+y+z=6$
Plug in $x= 1+3t,y=-2t,z=1+t$, we get
$t=2$
Thus,
$x= 1+3(2),y=-2(2),z=1+(2)$
Point of intersection: $(7,-4,3)$
