Determine if the lines L1and L2 given below are parallelinte

Determine if the lines L_1and L_2 given below are parallel,intersecting or skew.If they are intersecting,find the intersecting point.

The slope of L₁ is (3,-2,1) and the slope of L₂ is (1,-5,-1)

Since these are not proportional to each other, the lines are not parallel

So, they are either skew or intersecting

To check whether they are intersecting or not, we need to check the existence of (t₀, s₀) such that

3t₀ + 4 =s₀ -1,

-2t₀ -6 =-5s₀ +6,

t₀ + 4 =-s₀ +5

On solving the above equations,we get

t₀ =-1,s₀ =2

So, the intersection point is (1,-4,3).