Mark against the correct answer in each of the following:
The equation of the plane passing through the point A(2, 3,4) and parallel to the plane 5x - 6y + 7z = 3, is
Given: Point A(2, 3, 4) lies on a plane which is parallel to 5x – 6y + 7z = 3
To find: Equation of the plane
Formula Used: Equation of a plane is
a(x – x1) + b(y – y1) + c(z – z1) = 0
where a:b:c is the direction ratios of the normal to the plane
(x1, y1, z1) is a point on the plane.
Explanation:
Since the plane (say P1) is parallel to the plane 5x – 6y + 7z = 3 (say P2), the direction ratios of the normal to P1 is same as the direction ratios of the normal to P2.
i.e., direction ratios of P1 is 5 : -6 : 7
Let the equation of the required plane be
a(x – x1) + b(y – y1) + c(z – z1) = 0
Here a = 5, b = -6 and c = 7
Since (2, 3, 4) lies on the plane,
5(x - 2) – 6 (y - 3) + 7 (z - 4) = 0
5x – 6y + 7z – 10 + 18 – 28 = 0
5x – 6y + 7z = 20
The equation of the plane is 5x – 6y + 7z = 20