The discussion centers on interpreting the vector calculus problem involving two distinct points A and B in Euclidean space and finding the surface represented by the equation \(\vec{AM} \cdot \vec{MB} = 0\). Participants clarify that M is a point, not a scalar, and explore the implications of the dot product leading to the conclusion that the locus of points M forms a sphere. The final equation derived is \(x^2 + y^2 + z^2 = a(x-p) + b(y-q) + c(z-r)\), confirming that the surface defined is indeed a sphere.
PREREQUISITESStudents and educators in mathematics, particularly those studying vector calculus and geometry, as well as anyone seeking to deepen their understanding of spatial relationships in Euclidean space.
petertheta said:I get it. so I could descibe the surface as a sphere with a centre... and radius... which I deduce algebraically?