# intersection point line with 3d parabolic

I try to find intersection point between line and Paraboloid surface in 3D. I have 2 point on the line (x1,y1,z1) (x2,y2,z2) and the Paraboloid equation namely the Q matrix from here: http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/geometry/simple.html

How can I find the intersection between them?

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Ok I find the answer We calculate the normal vector from $p_1$ to $p_2$ $(a_p, b_p, c_p)$ and then we can calculate:
$x=x_1+at$
$y=y_1+at$
$z=z_1+at$