. Meeting Point of a Line and a Plane Theorem . The position vector of the point of intersection of the straight line r tb and the plane r n is a n b n + , provided b n ¹ Proof Let r tb be the equation of the given line which is not parallel to the given plane whose equation is r n . So, b n ¹ Vector - - Applications of Vector Algebra Let u be the position vector of the meeting point of the line with the plane.
Then u satisfies both r tb and r n for some value of t , say t . So, We get u tb ... ( ) u n ...( ) Sustituting ( ) in ( ), we get t b or a n t b n or a n b n ...( ) Sustituting ( ) in ( ), we get u a n b n b b n ≠ Example . Find the coordinates of the point where the straight line intersects the plane Here, , The vector form of the given plane is