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

[helpm3pl3ase]

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??

 

[Dick]

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.

 

[helpm3pl3ase]

<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

 

[Dick]

Better. Did you check by substituting your result back into the plane equations?

 

[helpm3pl3ase]

yes it worked, got 5 and 15

 

[Dick]

yes it worked, got 5 and 15

Good!