Q. 205.0( 1 Vote )

Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane .

Answer :

The required plane is parallel to , so required plane and the given plane must have the same normal vector.


Vector normal to the plane is



The required plane is passing through a given point


(a, b, c), so can write the position vector of the point as


Now, the equation of the required plane is given by,






(x - a) + (y - b) + (z - c)=0


x + y + z - (a + b + c)=0


x + y + z = a + b + c


Hence, the equation of the plane passing through (a, b, c) and parallel to the plane is i.e. (in vector form), or, in general form x + y + z = a + b + c.


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