Are There Other Equations for Lines Besides <x0+at,y0+by,z0+tz>?

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I have a question about the equation of a line

Are the forms <x0+at,y0+by,z0+tz>
And t=(x-x0)/a=(y-y0)/b=(z-z0)/c only for straight lines?
 
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hi nameVoid! :smile:

(i think you mean <x0+at,y0+bt,z0+ct>)
nameVoid said:
I have a question about the equation of a line

Are the forms <x0+at,y0+by,z0+tz>
And t=(x-x0)/a=(y-y0)/b=(z-z0)/c only for straight lines?

yes …

now show us how you'd prove that :wink:
 
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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