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#1 2011-12-17 07:22:27
- juantheron
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- Registered: 2011-10-19
- Posts: 312
volume
i have a question if a plane ax+by+cz+d=0 intersect coordinate axis at A, B,C , then what is the valume formed by ABC
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#2 2011-12-17 08:42:37
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: volume
hi juan
i got d^3/(6abc) 
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#3 2011-12-17 23:55:38
- juantheron
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- Registered: 2011-10-19
- Posts: 312
Re: volume
thank anonimnystefy
but how can you get it
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#4 2011-12-18 05:25:02
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: volume
well first of all you didn't state the problem correctly so i had to assume the you were talking about the pyramid ABCO. first of all the coordinates of A are (-d/a,0,0) because y and z coordinates have to be zero (the point lies on the x-axis). in the same manner you get that the coordinates of B and C are (0,-d/b,0) and (0,0,-d/c) respectively.if we take the triangle ABO to be the base of the pyramid and OC to be the height the we get the volume:
V=1/3 * OC * S(ABO) . . . where S(ABO) stands for the surface of the triangle ABO.
OC=d/c . . . because that's the distance between O and C.
S(ABO)=1/2 * OA*OB=1/2 * d/a * d/b=d^2/(2ab)
so
V=1/3 * d/c * d^2/(2ab) = 1/3 * d^3/(2abc)= d^3/(6abc)
you're welcome
Last edited by anonimnystefy (2011-12-18 05:25:35)
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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