# Equation of plane given points

ParoXsitiC

## Homework Statement

Find equation of plane containing points: (1,1,5),(3,5,3),(8,8,1),(10,2,2),(18,6,-1),(-1,-3,6)

## Homework Equations

Find 2 vectors given 3 points, using a common point. The cross product of these 2 vectors will be the normal vector of the plane. Use normal vector coords <a,b,c> as coefficients in the ax+by+cz=d formula where x,y,z is any point in the plane and solve for d. This equation better be true for all points.

## The Attempt at a Solution

P = (1,1,5)
Q = (3,5,3)
R = (8,8,1)

PQ = <2,4,-2>
PR = <7,7,-4>

PQ x PR = <-2,-6,14>

Plug in point P into formula and get:

-2x-6y+14z = 62

Test formula by plugging in Q and don't get 62.

aftershock
Check the z-component of your cross product result.

ParoXsitiC
Check the z-component of your cross product result.

Okay I had 14 when should be -14

PQ x PR = <-2,-6,-14>

Plug in point P into formula and get:

-2x-6y+14z = -78

Now point Q works out to be -78 but the point (10,2,2) turns out to be -60

Is this a trick question?

aftershock
Okay I had 14 when should be -14

PQ x PR = <-2,-6,-14>

Plug in point P into formula and get:

-2x-6y+14z = -78

Now point Q works out to be -78 but the point (10,2,2) turns out to be -60

Is this a trick question?

I just used point p and the normal vector we now agree on to form the equation of a plane and got something different than what you have. You might have messed up the algebra.

ParoXsitiC
I just used point p and the normal vector we now agree on to form the equation of a plane and got something different than what you have. You might have messed up the algebra.

I forgot to update the formula with -14:

-2x-6y-14z = -78

Still when using (10,2,2) I get -60 and not -78

aftershock
I forgot to update the formula with -14:

-2x-6y-14z = -78

Still when using (10,2,2) I get -60 and not -78

Yeah that is weird, are you sure they mean all the points are in the same plane?

ParoXsitiC
Yeah that is weird, are you sure they mean all the points are in the same plane?

That is how it is worded, reading it word for word. I thought it was weird too given 6 points instead of the common 3