Vector Calc Easy Q: Solutions Here

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thanks
 
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calculusisrad said:
Find c such thy v=I+2j-k and w=-I +5j +ck are perpendicular.

Is this right?
V * w = 0 (dot product)
So set the dot product equal to 0 and solve to get c = 9 ?

Or is it more complicated?

Thanks
That's the way to do it !

Also, a force of 50 lbs is directed 50 deg above horizontal, pointing right. Determine horizontal and vertical components and display results in a figure.

I used the pythagorean theorem to get horizontal= 50cos50 and so on for vertical. But I don't get how to draw the forces, the book shows them at weird angles but I thought they would just be drawn horizontally and vertically?

Thanks!
This is also correct.
 
calculusisrad said:
Find c such thy v=I+2j-k and w=-I +5j +ck are perpendicular.

Is this right?
V * w = 0 (dot product)
So set the dot product equal to 0 and solve to get c = 9 ?

Or is it more complicated?

Thanks

nope, that's exactly what you do.



Also, a force of 50 lbs is directed 50 deg above horizontal, pointin right. Determine horizontal and vertical components and display results in a figure.

I used the pythagorean theorem to get horizontal= 50cos50 and so on for vertical. But I don't get how to draw the forces, the book shows them at weird angles but I thought they would just be drawn horizontally and vertically?

Thanks!

i agree with you. i can't speak for what the book has drawn.
 
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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