The force represented by $5 j + k$ is acting through the point $9 i - j + 2 k .$ Find the moment about the point $3 i - 2 j + k$

3 i + 11 j + 15 k

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- 3 i - 11 j - 15 k

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- 4 i - 6 j + 30 k

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3 i + j + 15 k

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Solution

The correct option is C $- 4 i - 6 j + 30 k$
Here, $F = 5 j + k, O = 3 i - 2 j + k, P = 9 j - j + 2 k .$
$∴ r = \to O P = P . V$ of $P - P . V o f$ O
$= (9 i - j + 2 k) - (3 i - 2 j + k) = 6 i + j + k .$
$∴$ Moment, $M = r \times F = (6 i + j + k) \times (5 j + k)$
$= ∣ ∣ ∣ ∣ \begin{matrix} i & j & k 6 & 1 & 1 0 & 5 & 1 \end{matrix} ∣ ∣ ∣ ∣ = - 4 i - 6 j + 30 k .$

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