Two coplanar lines and finding the equation

[gundamshadow]

Homework Statement

Two coplanar lines, a and b are perpendicular to each other. a passes through the points (3,2,3) and (8,10,6). Find the equation for b if it passes through the point (7,49,25).

Homework Equations

The equation were trying to find is r = [x,y,z] + s [x1,y1,z1] + t [x2,y2,z2]

The Attempt at a Solution

Basically since the coordinates are perpendicular I used the cross product to find one direction vector. For my position vector I used (3,2,3). Now I'm not sure what to do with the last point (7,49,25) or what to do to find my second direction vector. I'm not even sure if I did the first part right. Help would be appreciated thanks!

 

[gneill]

Homework Statement

Two coplanar lines, a and b are perpendicular to each other. a passes through the points (3,2,3) and (8,10,6). Find the equation for b if it passes through the point (7,49,25).

Homework Equations

The equation were trying to find is r = [x,y,z] + s [x1,y1,z1] + t [x2,y2,z2]

The Attempt at a Solution

Basically since the coordinates are perpendicular I used the cross product to find one direction vector. For my position vector I used (3,2,3). Now I'm not sure what to do with the last point (7,49,25) or what to do to find my second direction vector. I'm not even sure if I did the first part right. Help would be appreciated thanks!

Hi gundamshadow, Welcome to PF.

Your question, being mathematical in nature, would probably fair better in the Precalculus forum. But I can give you a hint or two here

The lines involved are said to be coplanar, and that plane must have a normal. A plane's normal has some nice properties involving vectors in the plane and cross and dot products. You might want to look into that

You might start by finding any two vectors in the plane from the given points...