Linear Algebra (Parametric Form)

tweety24
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Homework Statement



L1 : x = (0, 1, 2) + s(1, 0, 2)
L2 : x = (4, 2, c) + t(−2, 0, d)

If c = 5 & d = 0, find the point P on L1 and Q on L2 so that the distance between P & Q is the smallest possible.


Homework Equations



the point of intersection?


The Attempt at a Solution



well the lines aren't parallel or identical in this case so they must intersect at some point.
 
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You are thinking about two dimensions. In three dimensions non parallel lines don't have to intersect.
 
oh okayy...so then to start off would i need to find the determinant?
 
lol yeahh i am
 

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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