Intercept Form of a Plane – Equation and Example

Here you will learn intercept form of a plane equation with examples.

Let’s begin –

Intercept Form of a Plane

The equation of a plane intercepting lengths a, b and c with x-axis, y-axis and z-axis respectively is

\(x\over a\) + \(y\over b\) + \(z\over c\) = 1

Note :

1). The above equation is known as the intercept form of the plane, because the plane intercepts length a, b and c with x, y and z-axes respectively.

2). To determine the intercepts made by a plane with the coordinate axes we proceed as follows :

For x-intercept : Put y = 0, z = 0 in the equation of the plane and obtain the value of x. The value of x is the intercept on x-axis.

For y-intercept : Put x = 0, z = 0 in the equation of the plane and obtain the value of y. The value of y is the intercept on y-axis.

For z-intercept : Put x = 0, y = 0 in the equation of the plane and obtain the value of z. The value of z is the intercept on z-axis.

Example : Write the equation of the plane whose intercepts on the coordinates axes are -4, 2 and 3 respectively.

Solution : We know that the equation of a plane having a, b and c intercept on the coordinate axes is given by \(x\over a\) + \(y\over b\) + \(z\over c\) = 1

Here a = -4, b = 2, and c = 3. So ,the equation of the required plane is

\(x\over -4\) + \(y\over 2\) + \(z\over 3\) = 1 

\(\implies\)  -3x + 6y + 4z =12