Posted by Mary on .
Let S be the plane defined by x−4y−3z = −18, and let T be the plane defined by −2x+8y+7z = 41. Find the vector equation for the line where S and T intersect.
x 0 0
y = 0 + t0
z 0 0

Math  Linear Algebra 
Reiny,
1st one times 2
2x  8y  6z = 36
2nd
2x + 8y + 7z= 41
add them
z = 5
sub into 1st x  4y  15 = 18
x  4y = 3
x = 4y  3
let y = 0 , x = 3, z = 5 > point (0,3,5)
let y = 2 , x = 5, z = 5 > point (2,5,5)
so direction of line of intersection is (2, 8, 0)
using the point (2,5,5)
x = 2 + 2t
y = 5 + 8t
z = 5