Consider the direction vectors

L1: r(t) = (-3 + 3t)i + (3 + t)j v1 = 3 i + j

L2: r(t) = (4 + 4t)i + (2 - 12t)j v2 = 4 i - 12 j

If they are parallel then they are scalar multiples i.e. v1 = k v2

for some k --they are not since to match the j components you would have to mutiply v1 by -12 but then the i components wouldn't match

If they are perpindicular the dot dt product would be 0

v1*v2 = 12 - 12 = 0 so they are perpindicular

to find the point of intersection then it occurs at time t1 and t2

such that the x and y components match:

1) -3 +3t1 = 4 + 4t2

2) 3 +t1 = 2- 12t2

Mutiply 1) by3 and add to 2) -6 + 10t1 = 14 t1 = 2 use this in L1

the pt is (3,5)

To check note -1 = 4t2 t2 = -1/4 use this in L2

the point is (3,5)