Consider the information that you are given carefully, I will help.
The line is parallel to the plane defined by This means that it lies in and as you have correctly deduced, if we let the direction vector of be then we require that . Let be the plane defined by .
Now consider the intersection of and , Clearly is a line with direction vector , and furthermore is parallel with both and . For to have angle with we must have that and have angle since is parallel to , and is parallel with both and .
Thus, we require that
You have two conditions so far:
The final (third) condition on is rather artificial. Lets put the condition on so that we find a unit vector, that is the 3 conditions are then
I think that what I wrote above is correct; however, I am not sure why you are given the point through which the line must pass through, I believe its a red herring.