# Equation of plane given points

• ParoXsitiC
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.

## 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.

Check the z-component of your cross product result.

aftershock said:
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?

ParoXsitiC said:
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.

aftershock said:
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

ParoXsitiC said:
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?

aftershock said:
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