There are a couple of ways. I think the simplest would be to find the unit vector in the direction of <-3, -3, -12> and show that it adds to to make 0.

So the magnitude of the vector <-3,-3,-12> is . Thus the unit vector in the direction of <-3, -3, -12> is

.

You can easily see if you add this vector to the unit vector that the sum is 0.

-Dan