Find the vector equation of the plane through the point and parallel to the plane
Formula : Plane = r . (n) = d
Where r = any random point
n = normal vector of plane
d = distance of plane from origin
If two planes are parallel , then their normal vectors are same.
Therefore ,
Parallel Plane r . (2i – 3j + 5k) + 5 = 0
Normal vector = (2i - 3j + 5k)
∴ Normal vector of required plane = (2i - 3j + 5k)
Equation of required plane r . (2i - 3j + 5k) = d
In cartesian form 2x – 3y + 5z = d
Plane passes through point (3,4, - 1) therefore it will satisfy it.
2(3) – 3(4) + 5( - 1) = d
6 – 12 - 5 = d
d = - 11
Equation of required plane r . (2i - 3j + 5k) = - 11
r . (2i - 3j + 5k) + 11 = 0