How do I find the position vector for the line of intersection?

[ishterz]

Homework Statement

Two planes have equations
2x-y-3z=7
x+2y+2z=0

Find a vector equation for their line of intersection

The Attempt at a Solution

I haven't learned the vector product in class but read it and attempted it and got the direction vector 4i-7j+5k.
However, I don't know how to get the position vector of this.



Thank you for your help and time

 

[Sethric]

You have done most of the work. You did the vector product correctly, and have found the vector coordinates for a line parallel to the line of intersection. Now all you need is a point contained in both planes. The line of intersection will then be parallel to the direction vector you found and will run through that point. I recommend letting z = 0 and finding the point where the planes intersect in the x-y plane. If you have any problems, let us know.