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