Quick vector plane theory question.

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.

SammyS
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Homework Helper
Gold Member

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.

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