Can Someone Verify My Calc 3 Practice Exam Solutions?

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    Calc 3 Exam
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Calc 3 exam tomorrow! Check my solutions please!

Takeing a practice exam but don't have the solutions, anyone who could verify my solutions would be appriciated!

First problem

Find the scalar equation of the plane that passes through (2,-1,0) and is perpendicular to the line x=1-t, y=2+t, z=5

My solution
-x+y= -3

Second problem

Find the scalar equation of the plane that passes through the origin and is parallel to the plane x+2y-3z=4

My solution
x+2y-3z=0

More problems to follow. Thanks in advance for any help!
 
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both look good to me
 


sweet thanks!
 

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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