Reduce the equation of the plane 4x – 3y + 2z = 12 to the intercept form, and hence find the intercepts made by the plane with the coordinate axes.
Given :
Equation of plane : 4x – 3y + 2z = 12
To Find :
1) Equation of plane in intercept form
2) Intercepts made by the plane with the co-ordinate axes.
Formula :
If
is the equation of a plane in intercept form then intercept made by it with co-ordinate axes are
X-intercept = a
Y-intercept = b
Z-intercept = c
Given the equation of plane:
4x – 3y + 2z = 12
Dividing the above equation throughout by 12
This is the equation of a plane in intercept form.
Comparing the above equation with
We get,
a = 3
b = -4
c = 6
Therefore, intercepts made by plane with co-ordinate axes are
X-intercept = 3
Y-intercept = -4
Z-intercept = 6