Finding the Point of Intersection of a Line With a Plane

The line P has equationand we want to find the intersection of this line with the planeWe substitute the values offrom the line in terms of into the equation of the plane. We solve this to findthen substitute this value ofback into the equation of the line to find the point of intersection.

Example: Find the point of intersection ofwith the plane

From the line,Substitute these expressions into the equation of the plane.

Substitute this value ofinto the equation of the line:

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