Writing Vector <1,7> as Sum of 2 Vectors

Loppyfoot
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Homework Statement



Write the vector <1,7> as a sum of two vectors, one parallel to <2,-1> and one perpendicular to <2,-1>

Homework Equations


DOt Product


The Attempt at a Solution



I'm confused on where to begin this problem. Should I be using the dot product?

Thanks
 
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i think you should draw out the vectors as they make up a right angle triangle.
 
I got the answer:

<-2,1> and <3,6>
 

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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