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{\bf Question}

A force of 2 units acts through the point Q $(1,2,0),$ in the
direction of the vector $(3,4,-1).$  Find its moment about the
point A $(2,2,-2).$

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{\bf Answer}

${\bf M} = {\bf r} \times {\bf F}$

${\bf r} = \vec{AQ} = \vec{OQ} - \vec{OA} = (1,2,0) - (2,2,-2) =
(-1,0,2)$

${\bf F} = 2{\bf \hat F}$ (unit vector in direction of ${\bf F}$)

${\bf M}={\bf r}\times{\bf F}={\bf r}\times(2{\bf \hat F})=2{\bf
r}\times{\bf \hat F}$

${\bf \hat F} = \frac{(3,4,1)}{\sqrt{3^2 + 4^2 + (-1)^2}} = \left(
\frac{3}{\sqrt{26}},\frac{4}{\sqrt{26}},\frac{-1}{\sqrt{26}}\right)$

${\bf r} \times {\bf \hat F} = \left\{ \frac{-8}{\sqrt{26}},
\frac{5}{\sqrt{26}},\frac{-4}{\sqrt{26}}\right\}$


${\bf M} = {\bf r} \times {\bf } = \left( \frac{-16}{\sqrt{26}},
\frac{10}{\sqrt{26}},\frac{-8}{\sqrt{26}}\right)$


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