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Scalar and Vector Notation

A force F= ...

Question

A force $F = 3 j - 6 k$ passes through the point A: $4 i - 2 j - 9 k;$ find the moment of P about the point B whose position vector is $6 i - 7 k .$

6 (3 i - 2 j - k) .

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6 (- 2 i - 6 j - k) .

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6 (i + 4 j + 3 k) .

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6 (- i - 4 j - 3 k) .

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Solution

The correct option is A $6 (3 i - 2 j - k) .$
Here $F = 3 j - 6 k, A = 4 i - 2 j - 9 k, B = 6 i - 7 k$
$∴ r = B A = (4 i - 2 j - 9 k) - (6 i - 7 k) = - 2 i - 2 j - 2 k$
Hence required moment is $= r \times F = ∣ ∣ ∣ ∣ \begin{matrix} i & j & k - 2 & - 2 & - 2 0 & 3 & - 6 \end{matrix} ∣ ∣ ∣ ∣ = 18 i - 12 j - 6 k$

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Similar questions

\to A = 2 ˆ i + 4 ˆ j - 7 ˆ k

\to B = 4 ˆ i - 6 ˆ j + 4 ˆ k

P = 4 i - 3 k

2 i - 2 j + 5 k .

i - 3 j + 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}

a = i - 2 j + 3 k, b = 3 i - 6 j + 9 k

a = - 2 i - 4 k, b = i - 2 j - k, c = i - 4 j + 3 k

P = 2 i - 5 j + 6 k

Q = - i + 2 j - k

4 i - 3 j - 2 k

6 i + j - 3 k .

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