Question

find a vector that makes the same angle with respect to the y-axis that vector i + 3k makes with respect to the x-axis

Answer 1

i+3k makes an angle of arctan(3) with the x-axis

So, you want a vector that makes that same angle with the y-axis. That would be

j+3i or j+3k or any of the vectors that lie in the cone with axis on the y-axis and the appropriate vertex angle.