Find parametric equations given point and two planes

[getty102]

Homework Statement

Find the parametric equations through point (5,-1,3) parallel to the line of intersection between 2x-y+z=1 and 6x-y-z=3, where 0≤t≤1

Homework Equations

1. Find normal vectors for both planes
2. Take cross product of both normal planes
...

The Attempt at a Solution

normal to plane 1 is <2,-1,1>
normal to plane 2 is <6,-1,-1>

cross product to both normal vectors is (1+1)i-(-2+6)j+(-2+6)k
=2i-4j+4k=<2,-4,4>

I wasn't sure how to input the point or if I am on the right track?

 

[vela]

You're on the right track. What do the parametric equations for a line generally look like?