1. Tardigrade
  2. Question
  3. Mathematics
  4. The three planes x + y = 0, y + z = 0 and x + z = 0

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The three planes x + y = 0, y + z = 0 and x + z = 0

Three Dimensional Geometry

Solution:

The planes x + y = 0 i.e. x = - y and y + z = 0 i.e. z = -y meet in the line
$\frac{x}{1} = \frac{y}{-1} = \frac{z}{1}$ .
Any point on this line is (t, -t, t). This point lies in the plane x + z = 0 if t + t = 0 $\Rightarrow $ t = 0 .
So the three planes meet in a unique point (0, 0, 0).