Possible webpage title: Determining Parallel Vectors in R^6

brabusbrad
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Homework Statement



Which of the following vectors in R^6 are parallel to u= (-2, 1, 0, 3, 5, 1)?

a) (4,2,0,6,10,2)
b) (4,-2,0,-6,-10,-2)
c) (0,0,0,0,0,0)


I don't even know how to approach this. Can anyone help me please?

Thanks
Brad
 
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Vectors A and B are parallel if A dot B = |A||B|. So...
 
or vectors are parallel if:
a = kb for some k

so write this a set of equations & see if they are consistent
 
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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