Mark against the correct answer in each of the following:

The equation of a plane passing through the point A(2, -3, 7) and making equal intercepts on the axes, is

Given: A(2, -3, 7) is a point on the plane making equal intercepts on the axes.

Formula Used: Equation of plane is where (x, y, z) is a point on the plane and a, b, c are intercepts on x-axis, y-axis and z-axis respectively.

Explanation:

Let the equation of the plane be

… (1)

Here a = b = c = p (let’s say)

Since (2, -3, 7) is a point on the plane,

(1) becomes

p = 6

Therefore equation of the plane is

x + y + z = 6