Answer
$(0,7,9)$
Work Step by Step
Vector equation of a line joining the points with position vectors $r_0$ and $r_1$ is:
$r=(1-t)r_0+tr_1$
Put $r_0=\lt -3,1,0\gt$ and $r_1= \lt -1,5,6\gt $
$r=(1-t)\lt -3,1,0\gt+t \lt -1,5,6\gt$
$r=\lt -3+2t,1+4t,6t\gt$
Parametric equations of the line are:
$x= -3+2t,y=1+4t,z=6t$
As we are given the equation of the plane is:
$2x+y-z=-2$
Plug in $x= -3+2t,y=1+4t,z=6t$, we get
$t=1.5$
Thus,
$x= -3+2(1.5),y=1+4(1.5),z=6(1.5)$
Point of intersection: $(0,7,9)$
