Linear Algebra Question - Two Planes

carlodelmundo
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Homework Statement



http://carlodm.com/images/math1.png

My question is:

Isn't it possible for two planes to have one solution? Geometrically, what if their edges were touching and that was the extent of their intersection?
 
Last edited by a moderator:
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carlodelmundo said:

Homework Statement



http://carlodm.com/images/math1.png

My question is:

Isn't it possible for two planes to have one solution? Geometrically, what if their edges were touching and that was the extent of their intersection?

What's the 'edge' of a plane? I thought planes were unbounded and didn't have 'edges'?
 
Last edited by a moderator:
Oh. Right. I forgot that went infinite. The darn diagrams make it look like they have edges!
 
carlodelmundo said:
Oh. Right. I forgot that went infinite. The darn diagrams make it look like they have edges!

Tough to draw a picture of a plane without edges. Try to sympathise with the illustrators and forgive their lapses.
 

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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