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Addition of Vectors

Three forces ...

Question

Three forces $2 i + 3 j - 6 k$ , $2 i + 3 j - 4 k$ and $i - j + k$ are acting on a particle $(0, 1, 2)$ . the magnitude of the moment of forces about the point $(1, - 2, 0)$ is

A

4 \sqrt{26}

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B

5 \sqrt{26}

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C

5 \sqrt{23}

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D

None of the above

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Solution

The correct option is D None of the above
Radius vector= Final point $-$ Initial point $= - i - 3 j + 2 k$
Moment of forces = $(2 i + 3 j - 6 k) \times (i - 3 j - 2 k) + (2 i + 3 j - 4 k) \times (i - 3 j - 2 k) + (i - j + k) \times (i - 3 j - 2 k)$
= $(- 24 i - 2 j - 9 k - 18 i - 9 k + 5 i + 3 j - 2 k = - 37 i + j - 20 k$
Magnitude is $\sqrt{(37)^{2} + 1 + (- 20)^{2}} = \sqrt{1770}$

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i + 2 j - 3 k, 2 i + 3 j + 4 k

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