I've been reading up on these three recently, and wondered if anyone could confirm what I think they do. I'm not 100% I understand these. del [tex](\bigtriangleup)[/tex], when applied to a scalar, creates a vector with that scalar as each of the XYZ values. eg [tex]\bigtriangleup . x = (x,x,x)[/tex] [tex]\bigtriangleup . 3 = (3,3,3)[/tex] divergence is applied to a vector, and sums the components of the vector into a scalar. eg [tex]\bigtriangleup . (x,y,z) = x+y+z [/tex] [tex]\bigtriangleup . (1,2,3) = 1+2+3 = 6 [/tex] finally, laplacian. This is the one I'm not as sure about. It's applied to a scalar I think? [tex]\bigtriangleup ^2 = \bigtriangleup(\bigtriangleup) [/tex] [tex]\bigtriangleup ^2 . x = \bigtriangleup(\bigtriangleup . x) [/tex] [tex]= \bigtriangleup((x,x,x)) [/tex] [tex] = 3x [/tex] That doesn't seem right (I think I'm meant to end up with a vector). Can laplacian be broken up like that or does it have a special rule?