Find cartesian equations of the line of intersection of the planes

[ezsmith]

Homework Statement

Find cartesian equations of the line of intersection of the planes x+3y-6z =2 and 2x+7y-3z=7

The Attempt at a Solution

What I did first was I cross product the 2 equation and then I got 33i-9j+k
Then I took both of the equation and let y = 0. After that my answer seems to be weird.. Did I did anything wrong? The answer of the book was given ∴x+7/33 = y-3/-9 = z

 

[vela]

Homework Statement

Find cartesian equations of the line of intersection of the planes x+3y-6z =2 and 2x+7y-3z=7

The Attempt at a Solution

What I did first was I cross product the 2 equation and then I got 33i-9j+k
Then I took both of the equation and let y = 0. After that my answer seems to be weird.. Did I did anything wrong? The answer of the book was given ∴x+7/33 = y-3/-9 = z

What do you mean by weird? In any case, your method, at least to me, seems to be a bit of overkill. Why not just solve the system of equations the usual way?

 

[ezsmith]

What do you mean by weird? In any case, your method, at least to me, seems to be a bit of overkill. Why not just solve the system of equations the usual way?

Never mind. I managed to solve it. Thank you for the reply :)