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Q.
The moment about the point $\hat{ i }+2 \hat{ j }+3 \hat{ k }$ of a force represented by $\hat{ i }+\hat{ j }+\hat{ k }$ acting through the point $2 i +3 j +$ $k$ is
Vector Algebra
Solution:
Here, $r=(2 i+3 j+k)-(i+2 j+3 k)$
$\Rightarrow r = i +\hat{ j }-2 \hat{ k }$ and $F = i +\hat{ j }+\hat{ k }$
Then, the required moment is given by
$r \times F=(i+\hat{j}-2 \hat{k}) \times(i+\hat{j}+\hat{k})=\begin{vmatrix}
\hat{i} & \hat{j} & \hat{k} \\1 & 1 & -2 \\1 & 1 & 1\end{vmatrix}=3 \hat{i}-3 \hat{j}$
$\therefore $ Moment about given point $=3 \hat{ i }-3 \hat{ j }$