Confused just a little bit though difference between (x,y), and <x,y>

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confused... just a little bit though... difference between (x,y), and <x,y>

the first one is a scalor, and the second one is a vector, but how...i'm not even sure how to say it...the second one with the <> what does the number mean if they're not coordinates?

thanks
 
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The use of brackets can vary a lot -- you'll have to consult whatever you're reading to find out if it explicitly states what it means by round and by angle brackets.

If that fails, you can try and figure it out by context, or maybe post some passages here so that we can guess.
 


Actually, the first one (x,y) is sometimes used as vector coordinates. It should be clear from the context. The numbers associated with the vector <x, y> gives two important pieces of info: (1) direction, and (2) magnitude. There should be a lot of info on the web to learn more for this basic concept.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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