Question P2.9: In each case, set up the dot product to find the magnitude o......
In each case, set up the dot product to find the magnitude of the projection of the force F along a-a axes.
Do not calculate the result.
Step-by-Step
a.
\begin{aligned} & \mathbf{F}= 300 \mathrm{~N}\left(\frac{2}{3} \mathbf{i}+\frac{2}{3} \mathbf{j}-\frac{1}{3} \mathbf{k}\right)=\{200 \mathbf{i}+200 \mathbf{j}-100 \mathbf{k}\} \mathrm{N} \\ & \mathbf{u}_{a}=-\frac{3}{5} \mathbf{i}+\frac{4}{5} \mathbf{j} \\ & F_{a}=\mathbf{F} \cdot \mathbf{u}_{a}=(200)\left(-\frac{3}{5}\right)+(200)\left(\frac{4}{5}\right)+(-100)(0) \\ & \quad \mathbf{b} . \mathbf{F}=500 \mathrm{~N}\left(-\frac{4}{5} \mathbf{j}+\frac{3}{5} \mathbf{k}\right)=\{-400 \mathbf{j}+300 \mathbf{k}\} \mathrm{N} \\ & \mathbf{u}_{a}=-\frac{1}{3} \mathbf{i}+\frac{2}{3} \mathbf{j}+\frac{2}{3} \mathbf{k} \\ & F_{a}=\mathbf{F} \cdot \mathbf{u}_{a}=(0)\left(-\frac{1}{3}\right)+(-400)\left(\frac{2}{3}\right)+(300)\left(\frac{2}{3}\right) \end{aligned}
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