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3D simaltaneous equations. watch

1. How do I know if the planes form a rectangular prism or a sheaf or whatever else?

for example:
x+y+z = 4
2x+3y-4z=3
5x+8y-13z=8

This apparently forms a rectangular prism. I can see that if you do elimination of say, x, they are inconsistent, but how do you tell the planes form a rectangular prism?
2. (Original post by ziroic)
How do I know if the planes form a rectangular prism or a sheaf or whatever else?

for example:
x+y+z = 4
2x+3y-4z=3
5x+8y-13z=8

This apparently forms a rectangular prism. I can see that if you do elimination of say, x, they are inconsistent, but how do you tell the planes form a rectangular prism?
Well, what are the defining features of a rectangular prism?

Although, I can't see how 3 planes would define one. I would have thought a right angle prism perhaps.
3. (Original post by ghostwalker)
Well, what are the defining features of a rectangular prism?

Although, I can't see how 3 planes would define one. I would have thought a right angle prism perhaps.

is it to do with sets of parrael lnies?
4. (Original post by ziroic)
is it to do with sets of parrael lnies?
Yes, all the edges along the length of the prism will be parallel to each other.

But, for a rectangular prism you will need 6 planes and need to be able split them into 3 sets of two, such that the two in each set are parallel to each other, and planes in different sets are perpendicular to each other.

So it's not a rectangular prism.

For a right angle prism you will need to show that the three places, pairwise meet in distinct lines that are parallel to each other, and that two of the planes are perpendicular to each other.
5. (Original post by ghostwalker)
Yes, all the edges along the length of the prism will be parallel to each other.

But, for a rectangular prism you will need 6 planes and need to be able split them into 3 sets of two, such that the two in each set are parallel to each other, and planes in different sets are perpendicular to each other.

So it's not a rectangular prism.

For a right angle prism you will need to show that the three places, pairwise meet in distinct lines that are parallel to each other, and that two of the planes are perpendicular to each other.

How do you show that the three lnies where the three planes meet are paralell?
6. (Original post by ziroic)
How do you show that the three lnies where the three planes meet are paralell?
They will have the same direction cosines.

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