How to Find the Projection of a Force Along the Y-Axis in 3D?

[pearss]

Homework Statement

I have a force in three dimensions such that:
F=600N
Alpha(angle with x axis) = 120
Beta(angle with y axis) = 60
Omega(angle with z axis) = 45

I'm to find the projection of F along the y axis.

The Attempt at a Solution

I found the force vector for this force by

F=F(cos120i+cos60j+cos45k)
F=600N(-.5i+.5j+.707k)
F= -300i+300j+424.2k

now i know to use a dot product between the force vector and the unit vector of the vector that I'm trying to find a projection onto...but since the vector is the y-axis I'm unsure about what to do from here.

I thought that u_OY = oy/magnitude oy

0i+j+0k / 1 = j

and a dot product between this and my force vector would just give me the y component of that force vector...300.

but I'm pretty sure this is wrong. does anybody have any hints? Thanks much

 

[nvn]

pearss: Your answer is correct. Nice work.

 

[pearss]

Thanks for the comfirmation nvn