Show that four points lie on a plane

[toupee]

Homework Statement

(2; 0; 1); (-1; 2; 3); (3; 2; 2) and (3;-6;-3)

Homework Equations

PS→⋅(PR→×PQ→)=0

The Attempt at a Solution

Hi all, I am just wondering if my calculations are correct, and in fact these points do not lie on a plane. My answer is = 50 and i am not confident. Can anyone help me please?

 

[Orodruin]

It would be much easier to judge if what you are doing is correct if you actually showed us what you are doing.

Edit: Also, the points do lie in a plane - any solution not resulting in this is going to be wrong.

 

[ehild]

Hi all, I am just wondering if my calculations are correct, and in fact these points do not lie on a plane. My answer is = 50 and i am not confident. Can anyone help me please?

What is 50?

ehild

 

[toupee]

I have miss-read the question. All it is asking me to do, is prove that these points lie in the same plane. May i ask how?

 

[Orodruin]

If this is a homework problem or problem in a course you are taking there should be a description of how to determine this in your course literature. Have you tried applying that?

 

[HallsofIvy]

I have miss-read the question. All it is asking me to do, is prove that these points lie in the same plane. May i ask how?

You have the answer in your first post:
PS→⋅(PR→×PQ→)=0
(I assume the arrow after indicates "vector")

Any three points, such as P, Q, and R must lie in a plane so the two vectors PR and PQ lie in a plane and their cross product is perpendicular to the plane. The fourth point, S, lies in that same plane if and only the vector PS does also- and then its dot product with the perpendicular vector is 0.