Help needed with direction angles and vector equations

[agenttiny200]

Homework Statement

A line has direction angles 60°, 45°, 60° and passes through the point
(1, -2, 5). Determine the vector equation of this line.

Homework Equations

I honestly have no clue. My teacher gave a hint it has to do with trig (as in the trig ratios) and the unit vector formula, but I don't see how they mix.

The Attempt at a Solution

Tried everything except the right way for the last week, resulting in dead ends.

 

[agenttiny200]

if no one has a clue, it would help to mention that, proving to my teacher that he should just give me the answer.

 

[agenttiny200]

And I am serious when I say I have been trying for a week to solve it, I am not trying to get by easily. posting my questions here is kind of a last resort, for a question that I am really stuck on.