The two line with equations L1: r = (1,2,-4) + t(k+1,3k+1,k-3) and L2: x=2-3s, y=1-10s, z=3-5s are given.
a. determine the value of k if this lines are parallel.
I tried to solved this but the correct answer is only -7, my answer is:
k+1 = -3 - -4
3k+1 = -10 - -11/3
k-3 = -5 - -2
because I took the t(k+1,3k+1,k-3) as tv(vector) and since it had to be parallel with the line, I took the vector from the other equation x=2-3s, y=1-10s, z=3-5s, which is -3,-10,-5 and i equated to the respective x y z in the first line...

Question

The two line with equations L1: r = (1,2,-4) + t(k+1,3k+1,k-3) and L2: x=2-3s, y=1-10s, z=3-5s are given.
 a. determine the value of k if this lines are parallel.
 I tried to solved this but the correct answer is only -7, my answer is:
 k+1 = -3 -> -4
 3k+1 = -10 -> -11/3 
k-3 = -5 -> -2 
because I took the t(k+1,3k+1,k-3) as tv(vector) and since it had to be parallel with the line, I took the vector from the other equation x=2-3s, y=1-10s, z=3-5s, which is -3,-10,-5 and i equated to the respective x y z in the first line...