Given that- r - 2i - 3j and F - 2i - 6j- The magnitude of torque N-m will be -

The correct option is A √(180) Given r=2î +3ĵ and Force F=2î +6ĵ And torqueτ =F× r =î #160; amp; ĵ #160; 2 amp; 3 2 ...

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Scalar and Vector Notation

Given that, ...

Question

Given that, $\to r = 2 ˆ i + 3 ˆ j$ and $\to F = 2 ˆ i + 6 ˆ j$ . The magnitude of torque (N-m) will be :

\sqrt{180}

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\sqrt{410}

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\sqrt{504}

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\sqrt{510}

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Solution

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\to F = (2 ˆ i - 3 ˆ j + 4 ˆ k) N

\to r = (3 ˆ i + 2 ˆ j + 3 ˆ k) m

F = (2 ˆ i - 3 ˆ j + 4 k)

r = (3 ˆ i + 2 ˆ j + 3 ˆ k)

τ = r \times F

\vec{r} \cdot (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) = 1 and \vec{r} \cdot (- \hat{i} + \hat{j}) = 4

\vec{r} \cdot (2 \hat{i} - \hat{j} + 2 \hat{k}) = 6 and \vec{r} \cdot (3 \hat{i} + 6 \hat{j} - 2 \hat{k}) = 9

\vec{r} \cdot (2 \hat{i} + 3 \hat{j} - 6 \hat{k}) = 5 and \vec{r} \cdot (\hat{i} - 2 \hat{j} + 2 \hat{k}) = 9

2 \hat{i} - 3 \hat{j} + 4 \hat{k} and - 4 \hat{i} + 6 \hat{j} - 8 \hat{k}

2 ˆ i - 3 ˆ j + 4 ˆ k

- 4 ˆ i + 6 ˆ j - 8 ˆ k

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