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Let (x-1)/2 = (y-2)/3 = (z-3)/4 = p
and (x-4)/5 = (y-1)/2 = z = q
express x , y, z in terms of p and q. we get 3 equations in 2 variables. Solve the first 2 equations and substitute in the 3rd. If it is true , then they intersect. The value of x,y,z gives the point of intersection.
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