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Find the parametric equations for the line of intersection of the planes x+y+z=3 and x-y+2z=2

I took the cross product of the 2 equations and got 3i-j-2k

I then set z=0 and got x=5/2 and y=1/2.
I got:
x=5/2 +3t

However, the answers are supposed to be:

What is my procedure missing to get there?

  • Calculus -

    I think your method is correct.
    You took the cross product of the two vectors of the plane <1,1,1>x<1,-1,2> and got the direction vector v=<3,-1,-2>

    You combined the two equations and got (0,5/2,1/2), which gives you the position

    There are many different solutions for an equation of a line. So don't think that your answer is wrong.

  • Calculus -

    *oops (5/2,1/2,0) for position

    Looking at the answer again,
    it looks like they divided the vector by 2

  • Calculus -

    Do you know why they divided it by 2?

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