The torque (τ→=r→×F→) of a force F→=−3i^+j^+5k^ acting at the point r→=7i^+3j^+k^ is

The torque is defined asτ=r×Fr×F=|i^j^k^731−315| =i^|3115|+j^|175−3|+k^|73−31| =i^(15−1)+j^(−3−35)+(7−(−9))=14i^−38j^+16k^

The torque (τ→=r→×F→) of a force F→=−3i^+j^+5k^ acting at the point r→=7i^+3j^+k^ is

The torque is defined asτ=r×Fr×F=|i^j^k^731−315| =i^|3115|+j^|175−3|+k^|73−31| =i^(15−1)+j^(−3−35)+(7−(−9))=14i^−38j^+16k^

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The torque $(\vec{τ} = \vec{r} \times \vec{F})$ of a force $\vec{F} = - 3 \hat{i} + \hat{j} + 5 \hat{k}$ acting at the point $\vec{r} = 7 \hat{i} + 3 \hat{j} + \hat{k}$ is

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

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

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

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

answer is A.

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Detailed Solution

The torque is defined as
$τ = r \times F$
$r \times F = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 7 & 3 & 1 \\ - 3 & 1 & 5 \end{matrix} |$
$= \hat{i} | \begin{matrix} 3 & 1 \\ 1 & 5 \end{matrix} | + \hat{j} | \begin{matrix} 1 & 7 \\ 5 & - 3 \end{matrix} | + \hat{k} | \begin{matrix} 7 & 3 \\ - 3 & 1 \end{matrix} |$

$= \hat{i} (15 - 1) + \hat{j} (- 3 - 35) + (7 - (- 9))$