Quick vector plane theory question.

[e_brock123]

Homework Statement

Hi I'm doing a question were I have 3 points and its asking me to find the normal to that plane, then it further asks to see if another point lies on that plane.

So due to reading the question I feel that it is suggesting that if I found the normal and then doted it with the point of interest it would let me know if it lies on the plane or not? I say this because my guess is the dot product could tell me if the normal and the point of interest are orthogonal meaning that the point does lie on the plane?

Any help will be greatly appreciated,
thanks.

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

Hi I'm doing a question were I have 3 points and its asking me to find the normal to that plane, then it further asks to see if another point lies on that plane.

So due to reading the question I feel that it is suggesting that if I found the normal and then doted it with the point of interest it would let me know if it lies on the plane or not? I say this because my guess is the dot product could tell me if the normal and the point of interest are orthogonal meaning that the point does lie on the plane?

Any help will be greatly appreciated,
thanks.

Homework Equations

The Attempt at a Solution

A point is not orthogonal to a vector. The point has no direction.

Construct a vector to or from this point to one of the other three. See if this vector is orthogonal to the normal.

 

[HallsofIvy]

If you are given three points in the plane then you can create two vectors, the vectors from one of the points to the other two. And, although you don't mention it, I assume you know that the cross product of those two vectors will be perpendicular to both and so to the plane.

As SammyS said, a point has no direction and can't be "perpendicular" to a vector. However, the vector from anyone of the original three points to the given fourth point can be. That will be perpendicular to the normal if and only if the fourth point lies on the plane.