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Wize University Physics Textbook (Master) > Force Vectors (Advanced Info)

Direction Cosine Angles

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Direction Cosine Angles / Directional Angles

Angles (α, β, ϒ): the angles between a vector and the positive x, y, or z axis.



Can now write the unit vector with direction cosine angles:

Then write the force vector A as:
A=AuAA=A_{uA}
A=Acos⁡αi+Acos⁡βj+Acos⁡γkA=A\cos\alpha i+A\cos\beta j+A\cos\gamma k
A=Axi+Ayj+AzkA=A_xi+A_yj+A_zk

AND when you are not given all 3 angles, use the identity to find the third angle:
cos2α+cos2β+cos2γ=1cos^2\alpha+ cos^2\beta +cos^2\gamma=1









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Write F2 in Cartesian Vector Form



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Given a 821.6N force vector acting with direction cosines of: alpha=72.8°, beta=83.3°, gamma=162°.
Represent the force in cartesian vector form.