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Previous Year Question (PYQs)



The moment of the couple formed by the forces $5\hat i+\hat k$ and $-5\hat i-\hat k$ acting at the points $(9,-1,2)$ and $(3,-2,1)$ respectively is





Solution

Moment of a couple $=\vec r \times \vec F$ $\vec r=(9,-1,2)-(3,-2,1)=(6,1,1)$ $\vec F=5\hat i+\hat k$ $\vec M=\begin{vmatrix} \hat i & \hat j & \hat k \ 6 & 1 & 1 \ 5 & 0 & 1 \end{vmatrix} = \hat i(1-0)-\hat j(6-5)+\hat k(0-5)$ $=\hat i-\hat j-5\hat k$


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