[western50]

The line in which the planes
x + y + z = 9, and
2 x - y - z = 3
intersect, is
3 x = 12 (or x = 4)... Is that true of false?

so what I figure out that the line for these two planes to intersect is line[t]={4,5,0}+ t{0,3,-3} = {4,5+3t,-3t}

So from these on can I separate them out and say that the line in which the planes intersect is x = 4?

[jcaron2]

In three dimensions, x=4 doesn't describe a line. It describes a plane. Based upon your calculations it's clear that the line of intersection does indeed lie within the x=4 plane (since x will come out to 4 regardless of what value of t you use), but that's not the same as saying "The line in which the planes ... intersect is x=4". Therefore, I'd say the answer is false.

If it said "The plane in which the two planes... intersect", on the other hand, I'd say the answer was true.

Do you agree?