Find an equation of the plane. The plane passes through the points (5, 3, 1) and (5, 1, -5) and is perpendicular to the plane 8x + 9y + 2z = 11.

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Find an equation of the plane. The plane passes through the points (5, 3, 1) and (5, 1, -5) and is perpendicular to the plane 8x + 9y + 2z = 11.

Mathematics
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I found the vector of two points, crossed points w/ a,b,c from eq of plane. then I plugged into eq. of plane formula. what did I do wrong?
Check your answer by taking dot product of two perpendicular vectors.
I see a mistake in my calculation.

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What is wrong in my method?
Show us your method.
(5,3,1) (5,1,-5) -> <0,-2,-6> <0,-2,-6>X<8,9,2>=<50,-48,16> <50,-48,16>.<8,9,2> = 0 <50,-48,16>=<25,-24,8> 25(x-5)^2-24(y-3)^2+8(z-1)=0 25x-125-24y-72+8z-8=0 25x-24y+8z=205
What does your answer say in book, apparently you are checking it?
chag (sorry to interrupt) did you ask about the calculus dream problem or was that someone else
Someone else.
k thanks
There is another method, I don't know if this is valid dot V=0. it gives you 25x-27y+2z=0
Not correct
You asked what is wrong with your method. The mistake is when you did the equation formula you squared x and y; you shouldn't have squared it 25x-24y+8z=? Plug in (5,3,1) and you get 25x-24y+8z=61

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