Posted by J on Monday, May 7, 2012 at 8:28pm.
We need the direction of their line of intersection....
double the 2nd plane equation, then add that to the 1st
x+2y-3z = -6
6x - 2y + 4z = 8
7x + z = 2
z = 2-7x
let x=1
then z = -5
back in the 1st
1 + 2y + 15 = -6
y = -11 -----------> point (1,-11,-5)
let x = 0
then z = 2
back in 1st
0+2y -6 = -6
y = 0 ------------> point (0,0,2)
direction vector of line of intersection of the planes = (1, -11, -7)
so one such vector equation is
r = (2,-1,7) + t(1,-11,-7)
(the question should have said, "Find a vector equation...."
since the answer I obtained is not unique)
We need the direction of their line of intersection? That's all the question mentioned... so is that still the correct answer? :/