Special Numbers in R3: a, b & c

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Homework Statement



"Whats special about vectors a, b, and c with respect to R3"

a= (1,2,-3)
b= (-2,5,8)
c= (1,3,5)

Homework Equations



N/A

The Attempt at a Solution



N/A, I see nothing special about them.
 
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Vectors can span a space, so maybe your vectors span R3. How could you check this?
 
Although it might be a spanning set I don't think that is the special property.
 

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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