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Rotational Work and Energy

Find the vect...

Question

Find the vector moment of three forces $i + 2 j - 3 k, 2 i + 3 j + 4 k$ and $- i - j + k$ acting on a particle at a point $P (0, 1, 2)$ about the point $A (1, - 2, 0) .$

- 2 i + 6 j - 10 k

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- (- 4 i - 2 j - 5 k)

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- (- 4 i - 2 j + 5 k)

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None of these

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Solution

The correct option is A $- 2 i + 6 j - 10 k$
Resultant force is, $F = (i + 2 j - 3 k) + (2 i + 3 j + 4 k) + (- i - j + k) = 2 i + 4 j + 2 k$
And $\to r = \to A P = - i + 3 j + 2 k$
Thus vector moment about A is, $\to r \times F = ∣ ∣ ∣ ∣ \begin{matrix} i & j & k - 1 & 3 & 2 2 & 4 & 2 \end{matrix} ∣ ∣ ∣ ∣ = - 2 i + 6 j - 10 k$

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Similar questions

\to i + \to 2 j + \to 3 k

\to i - \to 2 j + \to 5 k

\to 3 j - \to 4 k

- \to 2 i + \to 3 j - \to 3 k

\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = 3 \hat{i} + 2 \hat{j} + 7 \hat{k}, \vec{c} = 5 \hat{i} + 6 \hat{j} + 5 \hat{k}

\vec{a} = - 4 \hat{i} - 6 \hat{j} - 2 \hat{k}, \vec{b} = - \hat{i} + 4 \hat{j} + 3 \hat{k}, \vec{c} = - 8 \hat{i} - \hat{j} + 3 \hat{k}

\hat{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \hat{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, \hat{c} = \hat{i} - 3 \hat{j} + 5 \hat{k}

P = 4 i - 3 k

2 i - 2 j + 5 k .

i - 3 j + k .

\vec{a} = \hat{i} - \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k}, \vec{c} = λ \hat{i} - \hat{j} + λ \hat{k}

\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{c} = λ \hat{i} + λ \hat{j} + 5 \hat{k}

\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{b} = 3 \hat{i} + λ \hat{j} + \hat{k}, \vec{c} = \hat{i} + 2 \hat{j} + 2 \hat{k}

\vec{a} = \hat{i} + 3 \hat{j}, \vec{b} = 5 \hat{k}, \vec{c} = λ \hat{i} - \hat{j}

\to r = (1 \to i + 2 \to j + 3 \to k) + t (- 2 \to i + \to j + \to k)

\to r = (2 \to i + 3 \to j + 5 \to k) + s (\to i + 2 \to j + 3 \to k)

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