Equation of 3-dimensional plane

[stanford1463]

Homework Statement

Find the equation of the plane through vectors u=(1,1,2) parallel to the plane containing v=(2,2,-1), w=(1,-1,0), and the origin.

Homework Equations

The Attempt at a Solution

I did the cross product of v x w = (-1,-1,-4).
Thus, my equation became -x-y-4z=-9. Is this correct? Thanks.

 

[stanford1463]

bump...can anyone please see if I am right or wrong??

 

[gabbagabbahey]

bump...can anyone please see if I am right or wrong??

I'm not sure I understand the question here. Are you trying to find the equation of one plane (containing u) that is parallel to another plane (containing v,w. and the origin (0,0,0))? Or is there just one plane involved? Could you maybe repost the question in its original wording?

 

[Dick]

Homework Statement

Find the equation of the plane through vectors u=(1,1,2) parallel to the plane containing v=(2,2,-1), w=(1,-1,0), and the origin.

Homework Equations

The Attempt at a Solution

I did the cross product of v x w = (-1,-1,-4).
Thus, my equation became -x-y-4z=-9. Is this correct? Thanks.

Yes, vxw=(-1,-1,-4) is the normal to the plane. So the equation of the plane is -x-y-4z=C for some constant C. If I put (1,1,2) into that, I don't get -9.

 

[stanford1463]

Ok thanks! Yeah, it was a typo, I meant -10.