# Orthogonal projection of line onto plane

I have already read the post Orthogonal Projection of vector onto plane, but I have a different task. I need to make a notebook in Mathematica so that users are able to manually add parameters of an equation for a line and for a plane, given in the form $$x=x_1+t a_1, y=y_1+t a_2, z=z_1+ta_3$$, where $$(a_1,a_2,a_3)$$ are the coordinates of a vector parallel to the line and $$ax+by+cz+d=0$$ is the equation of the plane. I need to (1) return the equation of a projection and (2) obtain a graphic representation (a plot of the solution).

How could I modify the code in the previous topic to achieve this?

• What sort of parameters of "a line and space" will be provided? – J. M. is away Mar 23 at 14:12
• Edited the question so it could provide better information, I thought of parameters in the equations of the line and a plane – Anđela Todorović Mar 23 at 14:24
• Well, if you want to use the previous answer that you've referenced, the easiest thing to do is take off the arrowheads and extend the vector that is the projection in the negative direction. – mjw Mar 24 at 3:13