richyw Show that the line of intersection of the planes$x+2y-z=2\mbox{ and } 3x+2y+2z=7$is parallel to the line $\langle x,y,x \rangle = \langle 1+6t,3-5t,2-4t \rangle$ one year ago one year ago

1. richyw

my attempt at a solution. First I found normal vectors to the planes. $\vec{n}=\langle 1,2,-1 \rangle$$\vec{m}=\langle 3,2,2\rangle$then the cross product to get the vector parallel to that.$\vec{n}\times \vec{m} = \langle 6, -5, -4 \rangle$

2. richyw

so wouldn't this be the direction of the line formed by the intersection of the two planes?

3. richyw

so maybe what I am doing wrong is finding the direction of the second line. how would I do this? find two points on the line and then use the displacement vector?

4. richyw

NICE just figured it out myself, question closed.

5. mukushla

nice