Mark against the correct answer in each of the following:

If O is the origin and P(1, 2, -3) is a given point, then the equation of the plane through P and perpendicular to OP is


Given: P(1, 2, -3) is a point on the plane. OP is perpendicular to the plane.


Explanation:


Let equation of plane be ax + by + cz = d … (1)


Substituting point P,


⇒ a + 2b -3c = d … (2)



Since OP is perpendicular to the plane, direction ratio of the normal is (1, 2, -3)


Substituting in (2)


1 + 4 + 9 = d


d = 14


Substituting the direction ratios and value of ‘d’ in (1), we get


x + 2y – 3z = 14


Therefore equation of plane is x + 2y – 3z = 14

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