sanctus Posted January 16, 2008 Report Posted January 16, 2008 I have the following problem, from chapter 7 of:Principles of Computerized Tomographic Imaging [math]\vec{w}_1\cdot\vec{f}=p_1[/math]The hyperplane represented by this equation is perpendicular to the vector[imath]\vec{w}_1[/imath]. Why is this the case? Is there a theorem which states so? Drawings in 2 dimension let open many other possibilities or at least it looks like it. Quote
sanctus Posted January 16, 2008 Author Report Posted January 16, 2008 correction: the drawings show it (orthogonality between hyperplane and vec{w}) to be true. So there must be a theorem... Quote
Erasmus00 Posted January 16, 2008 Report Posted January 16, 2008 Think of the dot product relation as a projection, fixing only the component of f parallel to w. It does not fix the perpendicular component- hence the plane it is defining is going to perpendicular to w. -Will Quote
murad_math Posted January 20, 2008 Report Posted January 20, 2008 The thing is when ever there is an expressino equals constant, then it defines either a path or a surface, in this case you will get a single equation in multivariables, find the normal to this surface and then compare it with the vector w ,,, Quote
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