Find the torque of a force F = -3 i^ + j^ + 5k^ acting at the point r = 7 i^ + 3 j^+ k^

τ→=r×F=ijk731−315= i [3 x 5 -1 x 1] + j [1 x (-3) -7x 5] +k[7 x 1-3(-3)]=14i^-38j^+16k^

Find the torque of a force F = -3 i^ + j^ + 5k^ acting at the point r = 7 i^ + 3 j^+ k^

τ→=r×F=ijk731−315= i [3 x 5 -1 x 1] + j [1 x (-3) -7x 5] +k[7 x 1-3(-3)]=14i^-38j^+16k^

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Find the torque of a force F = -3 $\hat{i}$ + $\hat{j}$ + 5 $\hat{k}$ acting at the point r = 7 $\hat{i}$ + 3 $\hat{j}$ + $\hat{k}$

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14 $\hat{i}$ -38 $\hat{j}$ + 16 $\hat{k}$

4 $\hat{i}$ +4 $\hat{j}$ +6 $\hat{k}$

-21 $\hat{i}$ + 4 $\hat{j}$ + 4 $\hat{k}$

-14 $\hat{i}$ +34 $\hat{j}$ -16 $\hat{k}$

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Detailed Solution

$\vec{τ} = r \times F = |\begin{array}{ccc} i & j & k \\ 7 & 3 & 1 \\ - 3 & 1 & 5 \end{array}|$
= i [3 x 5 -1 x 1] + j [1 x (-3) -7x 5] +k[7 x 1-3(-3)]
=14 $\hat{i}$ -38 $\hat{j}$ +16 $\hat{k}$

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Find the torque of a force F = -3 i^ + j^ + 5k^ acting at the point r = 7 i^ + 3 j^+ k^

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Find the torque of a force F = -3 $\hat{i}$ + $\hat{j}$ + 5 $\hat{k}$ acting at the point r = 7 $\hat{i}$ + 3 $\hat{j}$ + $\hat{k}$