Q. 45.0( 1 Vote )
Find the vector equation of the plane passing through the point (1, 1, 1) and parallel to the plane 
Answer :
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 - j + 2k) = 5
Normal vector = (2i - j + 2k)
∴ Normal vector of required plane = (2i - j + 2k)
Equation of required plane r . (2i - j + 2k) = d
In cartesian form 2x - y + 2z = d
Plane passes through point (1,1,1) therefore it will satisfy it.
2(1) - (1) + 2(1) = d
d = 2 – 1 + 2 = 3
Equation of required plane r . (2i - j + 2k) = 3
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