Find the vector and Cartesian equations of the plane passing through the points(2, 2 –1), (3, 4, 2) and (7, 0, 6). Also find the vector equation of a plane passing through (4, 3, 1) and parallel to the plane obtained above.
Let A(2,2,-1), B(3,4,2) & C(7,0,6)
The equation of plane passsing through A(2,2,-1)
(3,7,2) & (7,0,6) lie of the plane
Solving equation (ii) and (iii), we get
putting the value of a, b and c in (i) we get
This is the required equation of the plane.
Now, the second plane passes through the point (4,3,1)
this plane is parallel to the above plane,
DR of the second plane be <5,2,-3>
So, the equation of the second plane