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  4. If the force represented by i + j + k is acting through the point 5 i +4 j -3 k, then its moment about the point (1,2,2) is

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Q. If the force represented by $i + j + k$ is acting through the point $5 i +4 j -3 k$, then its moment about the point $(1,2,2)$ is

Jharkhand CECEJharkhand CECE 2012

Solution:

We have, $F = i + j + k$ Let $P(5,4,-3)$ and $O(1,2,2)$ be given points. Then, $O P=4 i +2 j -5 k$
Now, moment of $F$ about $O$ $=r \times F\left|\begin{array}{ccc} i & j & k \\ 4 & 2 & -5 \\ 1 & 1 & 1\end{array}\right|=(2+5) i -(4+5) j +(4-2) k$