Parametric Equations for Line of Intersection of 3x-6y-2z=15 & 2x+y-2z=5

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SUMMARY

The discussion focuses on finding the parametric equations for the line of intersection of the planes defined by the equations 3x - 6y - 2z = 15 and 2x + y - 2z = 5. The correct parametric equations derived are x = 3 + 14t, y = -1 + 2t, and z = 15t. The solution was verified by substituting these equations back into the original plane equations, confirming that they satisfy both equations. The initial attempt at a solution was incorrect, highlighting the importance of verification in mathematical problem-solving.

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Homework Statement



Find parametric equations for the line in which the planes 3x − 6y − 2z = 15
and 2x + y − 2z = 5 intersect.


Homework Equations





The Attempt at a Solution



<2, 1, -2> - <3, -6, -2> = <-1, 7, 0>

x = 2 - t, y = 1 + 7t, z = -2

Did I do this correctly??
 
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Uh, no. Put the solution back into your two line equations. Does it work? I don't think so. Where did you find this 'solution method'? I think you should maybe try and find one that does.
 
<3, -6, -2> X <2, 1, -2> = <14, 2, 15>

Then set z to 0 to get x = 3, y = -1 ==> <3, -1, 0>

x = 3 + 14t
y = -1 + 2t
z = 15t
 
Better. Did you check by substituting your result back into the plane equations?
 
yes it worked, got 5 and 15
 
helpm3pl3ase said:
yes it worked, got 5 and 15

Good!
 

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