Find th intersection of two Lines of L1L2 with the following

Find th intersection of two Lines of L1,L2 with the following paramatric Equations.

L1: x=5+t,y=2t-2,z=-1-3t L2: x=2+s,y=2s,z=4-s

At the intersection of two line, the point of two line will be same. So the value of x, y. z will be same for both the line.

So, by equating x we get,

5 + t = 2 + s

or, s - t = 3 -----------------------------(1)

By equating z we get,

-1 - 3t = 4 - s

or, s - 3t = 5 -------------------------------(2)

Subtracting eqn-(2) from (1) we get,

2t = -2

or, t = -1

By putting value of t in eqn (1)

we get , s - (-1) = 3

or, s = 2

So in L1, x = 4 , y = -4 , z = 2

in L2, x =4 , y = 4, z = 2

Since both the point are not same,, there will not be any point of intersection