Find cartesian equations of the line of intersection of the planes

ezsmith
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Homework Statement


Find cartesian equations of the line of intersection of the planes x+3y-6z =2 and 2x+7y-3z=7

The Attempt at a Solution


What I did first was I cross product the 2 equation and then I got 33i-9j+k
Then I took both of the equation and let y = 0. After that my answer seems to be weird.. Did I did anything wrong? The answer of the book was given ∴x+7/33 = y-3/-9 = z
 
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ezsmith said:

Homework Statement


Find cartesian equations of the line of intersection of the planes x+3y-6z =2 and 2x+7y-3z=7

The Attempt at a Solution


What I did first was I cross product the 2 equation and then I got 33i-9j+k
Then I took both of the equation and let y = 0. After that my answer seems to be weird.. Did I did anything wrong? The answer of the book was given ∴x+7/33 = y-3/-9 = z
What do you mean by weird? In any case, your method, at least to me, seems to be a bit of overkill. Why not just solve the system of equations the usual way?
 
vela said:
What do you mean by weird? In any case, your method, at least to me, seems to be a bit of overkill. Why not just solve the system of equations the usual way?

Never mind. I managed to solve it. Thank you for the reply :)
 

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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