Force F=(3j - 4j + 12k)N acts at point A(1, -2, 3). Find - (i) Moment of force about origin (ii) Moment of forces about point B(2,1,2)m

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written 3.9 years ago by

teamques10 ★ 69k

• modified 3.9 years ago

engineering mechanics

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written 3.9 years ago by

teamques10 ★ 69k

(i) $Y_{OA}=1i-2j+3k\ m$

$\begin{align*}\therefore M_O^F&=\begin{vmatrix}i&j&k\\3&-4&12\\1&-2&3\end{vmatrix}\\[2ex]&=i(-4\times 3+2\times 12)-j(3\times 3-1\times 12)+k(-3\times 2+4\times 1)\\[2ex]&=12i+3j-2kNm\end{align*}$

(ii) $Y_{BA}=-i-3j+k\ m$

$\begin{align*}\therefore M_B^F&=\begin{vmatrix}i&j&k\\3&-4&12\\-1&-3&1\end{vmatrix}\\[2ex]&=i(-4+36)-j(3+12)+k(-9-4)\\[2ex]&=32i-15j-13kNm\end{align*}$

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