Find a vector parallel to two planes

[UrbanXrisis]

there are two planes:

3x+y+z=1
3x+z=0

find a vector U with positive first coordinate that is parallel to both planes.

the way I went about solving this:
the normal vectors are: <3,1,1> and <3,0,1>, the cross product of the vectors will give a vector perpendicular to the normal, which means it would be parallel to the two planes right?

 

[0rthodontist]

Yes, that's right.

 

[UrbanXrisis]

when I did this, I get <1,0,-3> and this is not correct. so i do not know where I went wrong

 

[0rthodontist]

(1, 0, -3) is correct. Maybe you are comparing it to a vector that is a multiple of (1, 0, -3)--there is more than one answer. (2, 0, -6) is also correct.