- #1
-Dragoon-
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Homework Statement
Find the parametric equations of the intersection line of two planes 2x - 3y - z + 1 = 0 and
3x - 2y + 3z - 4 = 0
Homework Equations
N/A
The Attempt at a Solution
First I'll label them:
2x - 3y - z + 1 = 0 [1]
3x - 2y + 3z - 4 = 0 [2]
Then I get rid of the z variable for now, and multiply [1] by 3 to do that, then eliminate by adding:
6x - 9y - 3z +3 = 0
3x - 2y + 3z - 4 = 0
_________________
9x - 11y - 1 = 0 [3]
Then I write y in terms of x:
y = (9/11)x - 1/11[4]
Then substitute [4] back into [1]:
2x - 3((9/11)x - 1/11) - z +1 = 0
2x - (27/11)x +3/11 - z + 1 = 0
Then write z in terms of x:
z = (-5/11)x + 14/11
Finally, I set x = t to write the parametric equations:
x = t
y = (9/11)t - 1/11
z = (-5/11)t + 14/11
However, this was the answer my book got:
x = (11/9)t + 1/9
y = t
z = (-5/11)t + 11/9
Can anyone help me figure out what I did wrong? I double checked all the tedious calculations, and they seem correct to me. Thanks in advance.