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MOMENT OF A FORCE ABOUT A SPECIFIED AXIS

\( \vec{M}_{a}=\vec{U}_{a} \cdot \overrightarrow {(r} \times \vec{F} ) \)

\( =\left|\begin{array}{lll}{U_{a_{x}}} & {U_{a_{y}}} & {v_{a_{z}}} \\ {r_{x}} & {r_{y}} & {r_{z}} \\ {F_{x}} & {F_{y}} & {F_{z}}\end{array}\right| \)

Determine the magnitude of the moment of the force  \(\mathbf{F}=\{300 \mathbf{i}-200 \mathbf{j}+150 \mathbf{k}\} \mathrm{N}\) about the  \(x\) axis.  Express the result as a Cartesian vector.

\( M_{x}=\vec{U}_{x} \cdot\left(\vec{r}_{B} \times \vec{F}\right) \)

\( =\left|\begin{array}{ccc}{i} & {j} & {k} \\ {1} & {0} & {0} \\ {0.3} & {0.4} & {-0.2} \\ {300} & {-200} & {150}\end{array}\right|=20 \mathrm{N.m} \)

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