I need to find the projection of vector onto the line that makes angle with , angle with and an acute angle with
If a line makes angles , , with the x, y, and z axes respectively, then the "direction cosines" satisfy and the vector is a unit vector in the direction of the line.
Here, so and .
so and .
That means that and so
A unit vector in the direction of the line is
Can you find the projection of your given vector onto that?