Understanding Differences in Constant Values for 3D Planes

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Homework Statement


My answer and the answer key in the textbook continue to differ by a constant d, which me and the book have opposites of. For instance, I found the vector to be

y-z=1 but the textbook says y-z= -1

also, I got 7x + y - 11z = -5, but the book says 7x + y - 11z = 5.

Do I have the wrong answer, or is it another form?
 
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It's completely impossible to say, unless you tell us what the question actually is.
 
Both questions ask you to find a plane that goes through a certain point and is either perpendicular or parallel to another plane or vector.
 
That's fine. But what is the actual question?
 
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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