PLAIN AND CIVIL: EXAMPLE 4.1.4: DOT PRODUCT: VECTOR PROJECTION

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

Take the vector of FAC by solving for its unit vector (both direction and scalar already solved in Example 2):

$\lambda _{AC}=\frac{2.5i-6j+2.33k}{6.905}=0.362i-0.869j+0.338k$

So

$\mathbf{F}_{AC}=F_{AC}\lambda _{AC}=60\left ( 0.362i-0.869j+0.338k \right )= 21.72i-52.14j+20.25k$

Also with the unit vector of strut AO:

$\lambda _{AO}=\frac{-6j-2k}{\sqrt{6^{2}+2^{2}}}=-0.949j-0.316k$

Thus, taking the dot product of Force AC and strut AO will give the component projection of FAC on axis AO.

$\left ( F_{AC} \right )_{AO}=\mathbf{F}_{AC}\bullet \lambda _{AO}$

$\left ( F_{AC} \right )_{AO}=\left ( 21.72i-52.14j+20.25k \right )\bullet \left ( -0.949j-0.316k \right )$

$\left ( F_{AC} \right )_{AO}=\left ( 21.72 \right )\left ( 0 \right )+\left ( -52.14 \right )\left ( -0.949 \right )+\left ( 20.25 \right )\left ( -0.316 \right )=43.06 lb$ ANSWER

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Tuesday 19 February 2019

EXAMPLE 4.1.4: DOT PRODUCT: VECTOR PROJECTION

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