A force $P = 4 i - 3 k$ passes through the point A whose position vector is $2 i - 2 j + 5 k .$ Find the moment of P about the point B whose position vector is $i - 3 j + k .$

M = 3 i - 19 j + 4 k .

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M = - 3 i + 19 j - 4 k .

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M = - 2 i + 21 j - 4 k .

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M = 2 i - 21 j + 4 k .

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Solution

The correct option is B $M = - 3 i + 19 j - 4 k .$
$- \to M = - - \to B A \times \to P$
$\to A = 2^i - 2^j + 5^k$
$\to B =^i - 3^j +^k$
$\to P = 4^i - 3^k$
Now,
$- \to M = (^i +^j + 4^k) \times (4^i - 3^k)$
$- \to M = - 3^i \times^k + 4^j \times^i - 3^j \times^k + 16^k \times^i$
$M = 3^j - 4^k - 3^i + 16^j$
$M = - 3^i + 19^j - 4^k$

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