Find the equation of plane parallel to 2x – 3y + z = 0 and passing through the point (1, – 1,2)?
Given Eq. of plane is 2x – 3y + z = 0 …… (1)
We know that equation of a plane parallel to given plane (1) is
2x – 3y + z + k = 0 …… (2)
As given that , plane (2) is passing through the point (1, – 1,2) so it satisfy the plane (2),
2(1) – 3( – 1) + (2) + k = 0
2 + 3 + 2 + k = 0
7 + k = 0
k = – 7
put the value of k in equation (2),
2x – 3y + z – 7 = 0
So, equation of the required plane is , 2x – 3y + z = 7