EXAMPLE 4.1.3: DOT PRODUCT: VECTOR PROJECTION

Determine the projected component of force FAB along the axis of strut AO.

Determining the component would require us to use the magnitude of the forces as given (). 

With only the magnitude known, we solve for the direction first to make Force AC into a complete vector. That is done by measuring the unit vector of the force.

                                                     

where

                                                   

From the computations in Example 1:





So vector for force AB converts to:




Next, determine the direction of the axis (strut AO) by its unit vector




Finally, the projected component is determined by using Dot Product of the force and the axis.








ANSWER


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