Equation for a plane question

Edit: Nevermind... Figured out where I went wrong, with a mistake in basic math that I kept overlooking for some reason...

Hello.

Ok, so I have three points, and I need to find the equation for the plane that contains those three points. The points are: A(2,0,2) C(√2,√2,2) and N(0,0,4). I am using the angle ACN for the calculation. CN=[-√2,-√2,2] and CA=[2-√2,-√2,0]. After I cross those two vectors, I get the normal, which is [√2,2-√2,√2]. I pick C as my on the plane coordinate, and plug it into the formula ax+by+cz+d=0, and get √2x+(2-√2)y+√2z+d=0, which then turns into (√2)(√2)+(2-√2)(√2)+2√2+d=0. That simplifies out to give me that d=-2-2√2. The problem is that the answer is supposed to be 8√2, according to our teacher. I have gone over this quite a few times now, and I simply cannot see where I have made an error... Can someone please take a look at it, and maybe see where I messed up? Thanks.

1 Attachment(s)

Re: Equation for a plane question

Your mistake is in the vector product. see the attached photo and redo the calculations again.

Attachment 29696

Re: Equation for a plane question

No, the vector product was fine, (everything was divided by two) but the problem was that when I was simplifying from (√2)(√2)+(2-√2)(√2)+2√2+d=0, I put it to 2+2√2-2+2+d=0. So I somehow overlooked that I made 2√2=2, which is clearly not correct.