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Question

Hi can someone help drawn an illustration for this problem

Consider a point P and plane through the point P0 with normal vector n.

(a) What do all the points satisfying the following condition have in common n *(vector formed from P0 to P)>0?

Thanks.

Answer 1

>>Consider a point P and plane through the point P0 with normal

>>vector n.

Imagine you have a sheet of cardboard, and you stick a needle into the surface (enough so that it will stand up by itself, but isn't pushed through to the other side) so that the needle is perpendicular to the surface of the plane.  The point of intersection is P0.  The needle is your vector n.

Stick a second needle into the same point on the cardboard, but on an angle this time.  Call the open end of this needle point "P".  The second needle itself is "the vector formed from P0 to P".

I'm assuming that they don't give you any information about P, so it could very well be outside of the plane.  The phrase "Consider a point P and plane through the point P0 with normal vector n" is a little amiguous as to whether or not P is in the vector n.