Posted by J on .
Find the vector equation of the line that passes through the point (2,1,7) and is parallel to the line of intersection of the planes x + 2y  3z = 6 and 3x  y + 2z = 4

Calculus 
Reiny,
We need the direction of their line of intersection....
double the 2nd plane equation, then add that to the 1st
x+2y3z = 6
6x  2y + 4z = 8
7x + z = 2
z = 27x
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) 
Calculus 
J,
We need the direction of their line of intersection? That's all the question mentioned... so is that still the correct answer? :/