The plane and the normal vector

Hi,
Why can’t we project the vector of our data point on the plane directly without using the normal plane.
I mean, Why can’t we do the dot product between the plane and the word vector instead of the dot product between the normal vector and the word vector.

Hi @Abdullah_Ayad

Normal vector represents the plane (normal vector n of the plane \pi is the vector to which all vectors in the plane \pi are perpendicular). By dot product (n \cdot v) you know which side of this plane \pi the vector v points. (vector by vector dot product results in a scalar).

How would you

dot product between the plane and the word vector instead

?

I guess what I’m asking is how else would you want to represent the plane? What would you want to dot product with?