Thread: vector help-->equation of planes

here's the question:

determine wheter or not a single plane passes through the following lines:

L1: [x-1, y-2, z+3]= k[-4, -1, 8] L2: [x, y,z] = [-11, -1, 21]+L[8,2, -16]

if a plane exists, find its scalar equ'n



plz help..

The lines obviously are parallel (the direction vectors are scalar multiples), so there is a plane that contains them. There are lots of ways to find the equation of that plane, but if you have technology at hand, the fastest way is probably to solve a system created by the points you can get out of your lines:

A(1) + B(2) + C(-3) + D = 0 (L1, k=0)

A(-3) + B(1) + C(5) + D = 0 (L1, k=1)

A(-11) + B(-1) + C(21) + D = 0 (L2, L=0)

A(-3) + B(1) + C(5) + D = 0 (L2, L=1)

Originally Posted by sweetbee

determine wheter or not a single plane passes through the following lines:
L1: [x-1, y-2, z+3]= k[-4, -1, 8] L2: [x, y,z] = [-11, -1, 21]+L[8,2, -16]
if a plane exists, find its scalar equ'n

I can show that the two equations represent the same line.
Can you?