What is the Value of s for Parallel Vectors in Linear Algebra?

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the vectors u and v are linearly independent. find s, if vectors (1-s)u - 2/3v and 3u +sv are parallel.

where u and v are vectors.

i am totally clueless, even my tutor couldn't solve it.
 
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How can you algebraically express that two vectors a and b are parallel?
Do that for the two vectors you are given (in function of s) and solve for s.
 
but u and v are coplanar? XD
 
Vectors a and b are parallel if there exists a scalair k such that a = kb. Apply that to the two vectors you want to be parallel, and find the s for which this holds.
 
byronsakic said:
the vectors u and v are linearly independent. find s, if vectors (1-s)u - 2/3v and 3u +sv are parallel.
where u and v are vectors.
i am totally clueless, even my tutor couldn't solve it.

You might consider getting another tutor! :)
 

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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