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**Intersection of 3 Lines in Space**

**1. 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.

**3. 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 cant even use cross product of directional vectors of L1 & L2.

Thanks for the help!

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