Finding Angle Bisector Vector in R3 Given V and U

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Homework Statement


given 2 vectors in R3 v(a,b,c), u(e,f,g) find the Angle Bisector vector


Homework Equations





The Attempt at a Solution


i just can't find the solution to this problem after working on it allot of time
please if you can help i am sure the solution is quite easy but i can't see it
 
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Normalize u and v to the same length, then take their average. How would you show that bisects the angle created by u and v?
 

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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