- #1
ace68
- 4
- 0
Intersection of 3 Lines in Space
L0 contains point P(1,0,2) and it meets
L1: x=y=z+2
L2: x+3=-y/2=z/3
Find equation of Line L0.
So we know that l1 and l2 are skewed.
Based on the given info:
L1) x=t
y=t
z=t-2
L2) x =t-3
y = -2t
z = 3t
these parametric eqns are the same eqns in vector form
r1 = (0,0,-2) + t(1,1,1)
r2 = (-3,0,0) + t (1,-2,3)
with P(1,0,2) for L0, i deduce
L0 = (1,0,2) + t(x,y,z)
im stuck now, with no directional vector since L0 is not necessarily perpendicular to both lines so i can't even use cross product of directional vectors of L1 & L2.
Thanks for the help!
Homework Statement
L0 contains point P(1,0,2) and it meets
L1: x=y=z+2
L2: x+3=-y/2=z/3
Find equation of Line L0.
The Attempt at a Solution
So we know that l1 and l2 are skewed.
Based on the given info:
L1) x=t
y=t
z=t-2
L2) x =t-3
y = -2t
z = 3t
these parametric eqns are the same eqns in vector form
r1 = (0,0,-2) + t(1,1,1)
r2 = (-3,0,0) + t (1,-2,3)
with P(1,0,2) for L0, i deduce
L0 = (1,0,2) + t(x,y,z)
im stuck now, with no directional vector since L0 is not necessarily perpendicular to both lines so i can't even use cross product of directional vectors of L1 & L2.
Thanks for the help!
Last edited: