13.6k views
4 votes
Ex. Find the co-ordinates of the points where the plane ax + by + cz + d = 0, a² + b² + c² does not equal to 0 meets the three co-ordinate axes.​

User Javis
by
8.7k points

1 Answer

7 votes

To find where the plane intersects the coordinate axes, set two of the variables to zero and solve for the third to find each axis intercept: x-intercept = (-d/a, 0, 0), y-intercept = (0, -d/b, 0), and z-intercept = (0, 0, -d/c).

To find the coordinates of the points where the plane ax + by + cz + d = 0 meets the three coordinate axes, we follow a simple procedure.

We calculate each intercept by setting the other two variables to zero and solving for the remaining one.

To find the x-intercept, set y = 0 and z = 0 in the equation. Solving ax + d = 0 for x gives us the x-intercept (x, 0, 0) where x = -d/a.

For the y-intercept, set x = 0 and z = 0. Solving by + d = 0 for y yields the y-intercept (0, y, 0) where y = -d/b.

To find the z-intercept, set x = 0 and y = 0. Solving cz + d = 0 for z provides the z-intercept (0, 0, z) where z = -d/c.

Considering a² + b² + c² ≠ 0 ensures that the plane is not parallel to any of the coordinate axes, allowing us to find distinct intercepts on each axis.

User Mirza Dobric
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories