This problem was confusing me so any help would be appreciated!

Write both the parametric and symmetric equations of the line of intersection of the planes with the equations 2x - y + z = 5 and x + y - z = 1.

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- Jul 15th 2007, 06:52 AMclockinglyParametric equations of plane problem
This problem was confusing me so any help would be appreciated!

Write both the parametric and symmetric equations of the line of intersection of the planes with the equations 2x - y + z = 5 and x + y - z = 1. - Jul 15th 2007, 07:42 AMThePerfectHacker
If then:

Thus, and

If then:

Thus, and

Thus, we have that this line must contains the points

Thus, the Symettric Equation is:

Note, this is a zero in the denominator of the first fraction, it is a useful notation I saw in a Russian Textbook* which simply means constantly, so it is just a shorthand notation.

*)If you are interested the Textbook was written by Perelman! Not Perelman you think it is but his grandfather! - Jul 15th 2007, 07:52 AMJhevon
- Jul 15th 2007, 07:57 AMThePerfectHacker
- Jul 15th 2007, 08:52 AMSoroban
Hello, clockingly!

Quote:

Write both the parametric and symmetric equations of the line of intersection

of the planes with the equations: .

We have: .

Add [1] and [2]: .

Substitute into [2]: .

We have as a function of

On the right side, replace with a parameter .

. . . . .*. . . There!*

- Jul 15th 2007, 08:55 AMJhevon
- Jul 15th 2007, 09:09 AMPlato
The customary notation used in textbooks in North America for the symmetric form in which one direction number is zero is to use a semicolon: .