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!

Printable View

- May 26th 2008, 10:19 AMmathstudent43Line 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! - May 26th 2008, 11:13 AMearboth
Solve the system for x and y dependent from z. I've got:

$\displaystyle x=-\frac1{12} - \frac16 z$ and $\displaystyle y = -\frac16 + \frac23 z$

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

$\displaystyle \left|\begin{array}{l}x = -\frac1{12} - \frac16 t \\ y= -\frac16 + \frac23 t \\z = t \end{array} \right.$

That means the vector equation of the line is:

$\displaystyle (x, y, z) = \left(-\frac1{12}~,~-\frac16~,~0\right) + t \cdot \left(-\frac16~,~ \frac23~,~1\right)$

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.