For the following problem: Find an equation of the plane that passes through the points A(2,1,1), B(-1,-1,10) and C(1,3,-4).
I found the normal vector to be <-8,-24,-8>
So then my equation would turn out to be: -8x -24y - 8z = -48
But somewhere when I was doing my homework a couple problems ago, I simplified the normal vector? Can that be done? would that be right? If I took <-8, -24, -8> and divide by -3 and get <1,3,1>, or is that for something totally different? Is the equation I got correct?
I found the normal vector to be <-8,-24,-8>
So then my equation would turn out to be: -8x -24y - 8z = -48
But somewhere when I was doing my homework a couple problems ago, I simplified the normal vector? Can that be done? would that be right? If I took <-8, -24, -8> and divide by -3 and get <1,3,1>, or is that for something totally different? Is the equation I got correct?
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You can use any vector that is normal to the plane. They will all be constant multiples of <-8, -24, -8>. So, yes using <1, 3, 1> is perfectly legitimate. You will get the same equation. Notice that if you divide the equation by -8 you get
x + 3y + z = 6
which gives the same plane.
x + 3y + z = 6
which gives the same plane.