Question
Find the vector equation of the plane passing through three points with position vectors 
Also, find the coordinates of the point of intersection of this plane and the line 
Solution
Let the position vectors of the three points be, 
So, the equation of the plane passing through the point 
So, the vector equation of the required plane is 
The equation of the given line is 
Position vector of any point on the given line is
....(2)
The point (2) lies on plane (1) if, 
Putting 
in (2), we have
Thus, the position vector of the point of intersection of the given line and plane (1) is 
and its co-ordinates are (1, 1, -2).
