Vector Equation Proof: Finding the Magnitude of a Vector Sum

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Homework Statement



Prove llu+vll2 + llu-vll2 =2llull2 + 2llvll2


Homework Equations



I am thinking I need to use some dot, or cross products.

The Attempt at a Solution



I just do not know where to start.
 
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Use what you know for finding the length of a vector (in terms of a dot product)and the associativity of the dot product.
 
What do you mean by that?
 
Baumer8993 said:
What do you mean by that?

||a||^2=a.a, use that.
 
Ohhh thanks! Now I get it.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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