Thread: Line of intersection of 3 planes.

Please help.

Find the vector equation of the line of intersection of the 3 planes represented by this system of equations.

2x - 7y + 5z = 1
6x + 3y - z = -1
-14x - 23y + 13z = 5

Thank you very much!

Originally Posted by mathstudent43

Please help.

Find the vector equation of the line of intersection of the 3 planes represented by this system of equations.

2x - 7y + 5z = 1
6x + 3y - z = -1
-14x - 23y + 13z = 5

Thank you very much!

Solve the system for x and y dependent from z. I've got:

and

Set z = t. Then you have the parametric equation of the intersection line:



That means the vector equation of the line is:



The first vector is the stationary vector of a point which is located in all three planes and the second vector is the direction vector of the line.