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A force $\vec{F} = (5 \hat{i} + 6 \hat{j}) N$ is acting at point $A (2 m, 4 m)$ . Then the moment of the force about the point $B (1 m, 1 m)$ in N-m is

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$7 \hat{j}$

$(8 \hat{i} - 6 \hat{j})$

$- 9 \hat{k}$

$- 6 \hat{k}$

answer is C.

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Detailed Solution

$\overset{⇀}{r_{A B}} =$ Position vector of A relative to B

$= (2 - 1) \hat{i} + (4 - 1) \hat{j} m = (\hat{i} + 3 \hat{j}) m$

$∴ {\vec{M}}_{B} = {\vec{r}}_{A B} \times \vec{F} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 3 & 0 \\ 5 & 6 & 0 \end{matrix} | N - m = - 9 \hat{k} N - m$

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