Find the equation of the plane whose x-intercept, y-intercept and z-intercept are 2, 3, 1. respectively.

Solution:

Intercepts of the plane are points on the x, y and z axis where the plane cuts their axes.

If the x-intercept of the plane is (a, 0, 0), y-intercept is (0, b, 0) and z-intercept is (0, 0, c) then the equation of the plane is x/a + y/b + z/c = 1.

Here, a = 2, b = 3, c = 1 

∴ x/2 + y/3 + z/1 = 1 ----(1)

Multiply equation(1) by 6

⇒ 3x + 2y + 6z = 6 ------(2)

Equation (1) represents the equation of the plane in intercept form.

Equation (2) represents the equation of the plane in the general form.

Find the equation of the plane whose x-intercept, y-intercept and z-intercept are 2, 3, 1. respectively.

Summary:

The equation of the plane whose x-intercept, y-intercept and z-intercept are 2, 3, 1 respectively, is x/2 + y/3 + z/1 = 6 in intercept form and 3x + 2y + 6z = 6 in general form.