Is the Vector Parametric Equation for Line L Perpendicular to Plane P?

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Homework Statement


Find the vector parametric equation of the line L passing through the point p=(1,2,3) and perpendicular to the plane P having equation 2x-3y-5z=7

Homework Equations


N/A

The Attempt at a Solution


q=P+tu

(where u is the vector of the normal)

[x,y,z]=(1,2,3)+t(2,-3,-5)

x= 1+2t
y= 2-3t
z=3-5t
 
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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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