A force of 1200N acts along PQ, P(4,5,-2) and Q(-3,1,6)m. calculate its moment about a point A(3,2,0)m

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written 3.9 years ago by

teamques10 ★ 69k

$F_{pq}=1200N\\[2ex] \Delta x=-3-4=-7\\[2ex] \Delta y=1-5=-4\\[2ex] \Delta z=6-(-2)=8\\[2ex] \therefore S=\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}=11.36\\[2ex] \therefore l=\dfrac{\Delta x}{S}=-0.62;m=\dfrac{\Delta y}{S}=-0.35;n=\dfrac{\Delta z}{S}=0.7\\[2ex] \therefore F_x=-744N;F_y=-420N;F_z=840N\\[2ex] \bar r_{AP}=(4-3)i+(5-2)j+(-2-0)k=i+3j-2k\\[2ex] M_A=\bar F\bar r$

$M_A=\begin{vmatrix}i&j&k\\744&420&840\\1&3&-2\end{vmatrix}$

$M_A=i(420(-2)-840\times 3)-j(744(-2)-840)+k(744\times 3-420)\\[2ex] M_A=-3360i+2328j+1812kNm$

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