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=AuA​  
A=Acos⁡αi+Acos⁡βj+Acos⁡γkA=A\cos\alpha i+A\cos\beta j+A\cos\gamma kA=Acosαi+Acosβj+Acosγk
                               A=Axi+Ayj+AzkA=A_xi+A_yj+A_zkA=Ax​i+Ay​j+Az​k

   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=1cos2α+cos2β+cos2γ=1

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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.

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Wize University Statics Textbook (Master) > Force Vectors

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