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Equation of plane given points

  • Thread starter ParoXsitiC
  • Start date
  • #1
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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.
 

Answers and Replies

  • #2
110
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Check the z-component of your cross product result.
 
  • #3
58
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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?
 
  • #4
110
0
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.
 
  • #5
58
0
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
 
  • #6
110
0
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?
 
  • #7
58
0
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
 

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