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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:

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:




and then placed in the data equation. We get one equation with one unknown- t .

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