Thread: Vector(3-Space) Word Problem Help

Problem:

Determine if the points P(3, -2, -7), Q(0 , 4, 2), R(-1, 3, -1) and S(5, -1, -3) are coplanar.

Answer in text: Yes

Additional Comments:

Please help me, I have a test tomorrow that basically decides my future.

Originally Posted by Morphayne

Problem:

Determine if the points P(3, -2, -7), Q(0 , 4, 2), R(-1, 3, -1) and S(5, -1, -3) are coplanar.

One very fast and easy way to check if a set of four points are coplanar is by putting them in a matrix and checking the determinant.

Four points, are coplanar if and only if



I don't have a proof of this off-hand, but it should work.

Jhevon is going to kill me for that

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By the way ^^

I suppose you're in high school and because you talked about linear systems, we'll do it this way :

The equation of a plane is

So write the linear system of equations assuming that P, Q, R and S are in this plane. Then solve for a,b,c and d.
If it has a (unique) solution, it will mean that the points are coplanar I'll let you do the working, because I really have to go to bed


Actually, this is equivalent to Reckoner's method, but his is for higher grades

Here is an easy if tedious way to check.
If then the four points are coplanar.