# Thread: [SOLVED] Equation of a Plane

1. ## [SOLVED] Equation of a Plane

I was reading a solution and got really confused trying to follow it. Here is what it said.

Find the equation of a plane passing through e(1,2,3), f(2,5,4) and g(3,4,6)
A normal to the plane is EF x FG (which I deciphered to mean (F-E) and (G-F)
since it then said (1,3,1) x (1,-1,2).

Now the part that really throws me off is here...it then says the answer is (7,-1,-4) therefore the equation is 7x - y - 4z = D. Afterwards they plugged in one of the points into the equation to get D.

But where did (7,-1,-4) come from?? Help, I'm so lost!

2. Originally Posted by a_desenhista
I was reading a solution and got really confused trying to follow it. Here is what it said.

Find the equation of a plane passing through e(1,2,3), f(2,5,4) and g(3,4,6)
A normal to the plane is EF x FG (which I deciphered to mean (F-E) and (G-F)
since it then said (1,3,1) x (1,-1,2).

Now the part that really throws me off is here...it then says the answer is (7,-1,-4) therefore the equation is 7x - y - 4z = D. Afterwards they plugged in one of the points into the equation to get D.

But where did (7,-1,-4) come from?? Help, I'm so lost!
you said the answer yourself. it comes from (1,3,1) x (1,-1,2)

you do know how to compute the cross-product of vectors, right?

just evaluate it like a determinant. you want to find:

$\displaystyle \left| \begin{array}{ccc} \bold{i} & \bold{j} & \bold{k} \\ 1 & 3 & 1 \\ 1 & -1 & 2 \end{array}\right|$ ...that is, the determinant