Finding equation of a plane passing through a point with given direction vectors

htoor9
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Homework Statement


I need to find the equation of a plane with direction vectors <1,3,-1>/sqrt(11) and <-2,1,1>/sqrt(6) passing through the point (1,2,3)


Homework Equations





The Attempt at a Solution


I'm not really sure what to do, I was considering taking the cross product, but I'm not sure what that would leave. Thanks
 
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The cross product of two tangent vectors would give you a normal vector, wouldn't it? Can't you find the equation of the plane from a normal vector and a point on the plane?
 

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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