Calculating 3D Component Vectors and Resultant Force for Inclined Forces

[yhumei]

Express each force as a Cartesian vector and then determine the resultant force F. Find the magnitude and coordinate direction angles of the resultant force and sketch this vector on th coordinate system.
There's a drawing of 1 force(F2) of magnitude 130N, along the negative z direction(-z), and another force(F1) of magnitude 80N, 40 degrees from the +x direction, 50 degrees from the -y direction and an incline of 30 degrees on the +z direction.



I want to know the component vectors of this force



I know how to find the component vectors of the forces using the x-axis direction and the y-axis directions only, I don't know the way to find the component vectors for the z-axis. (Which I think are (80sin40i and 80cos40j) if I am wrong please correct me.)

 

[kuruman]

Hi yuhumei and welcome to PF. Consider a plane defined by the z-axis and the vector. Draw your vector assuming that the paper is that plane. Can you find its z-component?

 

[lightgrav]

you're mis-interpreting the diagram ...
If those angles were really from the vector itself straight to each axis,
then (cos^2 + cos^2 + cos^2) has to = 1.
Probably, the "projection" of the 80N force onto the xy plane is 50deg from -y and 40deg from +x ... and the vector is 30deg from z .