% 	INNER PRODUCTGAfigure; clc; %/% 	INNER PRODUCT%global x B v w; %/clf; %/% 	The inner product of two vectors is a scalar % 	(its magnitude denotes the relative angle)%.v = e1;w = unit(e1 + e2);draw(v,'b'); %/GAtext(0.7*v - 0.1*unit(e2^v)/I3,'v'); %/draw(w,'g'); %/GAtext(0.7*w + 0.1*unit(e2^w)/I3,'w'); %/inner(v,w) %w% Geometrically, this is a zero-dimensional subspace:% a weighted point at the origin.draw(inner(v,w),'r'); %/draw(I3/100000,'r'); %/GAprompt; %/%.% 	The inner product x.B of a vector x and a bivector B is % 	a vector in B, perpendicular to x% 	(its magnitude denotes the relative angle)%.clf; %/x = unit(e1 + e3); draw(x,'b'); %/GAtext(0.7*x + 0.1*unit(e2^x)/I3,'x'); %/B = e1^e2; %% ===>  This is v^w, but we prevent unnecessary variables.%% ===>  Yet the labels are plotted using v,w in case we want to change this.draw(B,'y'); %/GAtext(-0.5*v+0.1*B/I3,'B'); %/inner(x,B) %waxis off; %/draw(inner(x,B),'r'); %/GAtext(inner(x,B)+0.1*B/I3,'x \bullet B'); GAprompt; %/ %	Spinning shows that x.B is "the part of B least like x".GAorbiter(-360,10); %/