I''m wondering if you calculus book is trying to pull a fast one on me here.... How would you normalize, say m = [1,1] or n = [2,3], using the good old u = v / |v| formula? Either my book is consequently bogus, or I''m consequently stupid (or both..). -meZ

|m| = sqrt(2).

unit(m) = (1/sqrt(2),1/sqrt(2))

|n| = sqrt(13).

unit(n) = (2/sqrt(13),4/sqrt(13))


Mike

That''s exactly what I''ve been claiming all along (*phew* not THAT stupid after all). The book OTOH (Calculus w/ Analytic Geometry by Edwards&Penney) consequently claims (ie. 50% of the cases) that

u = ( |v| / sqr(|v|) ) * v

giving:
m = [1/2 * sqrt(2), 1/2 * sqrt(2)]
n = [2/13 * sqrt(13), 3/13 * sqrt(13)]

Does this make any sense at all? Does it mean anything else?

-meZ

Yes, it makes perfect sense. (1/2)*sqrt(2) = sqrt(2)/2 = 1/sqrt(2). You can prove this by multiplying (sqrt(2)/2) * (sqrt(2)/sqrt(2)) = 2/(2*sqrt(2)) = 1/sqrt(2). Same thing for sqrt(13).


Mike

Aaah.. but of course!

Thanks alot!!!


Note-to-self: Switch brain to ON!