Finding the Direction of a Vector: Solving a Problem with Vectors

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ive been trying to do this problem but i don't know where to start...any help?


let v be a vector of length 9 in the direction 65degrees south of west.

if u has the same direction as v, and if 3|u| = 2|v|, then which of the following can be used to describe u?


u = 5.705i + 12.235j
u = -2.536i - 5.438j
u = 2.536i + 5.438j
u = -5.705i - 12.235j
none of these
 
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What is the magnitude of u? From that find the components of u.
 

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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