Solve this


A force $\vec{F}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ is applied on an intersection point of $\mathrm{x}=2$ plane and $\mathrm{x}$-axis. The magnitude of torque of this force about a point

$(2,3,4)$ is_____

(Round off to the Nearest Integer)



$\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}$

$\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}})-(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})=-3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$

$\& \overrightarrow{\mathrm{F}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$

$\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 0 & -3 & -4 \\ 4 & 3 & 4\end{array}\right|$


$=-16 \hat{\mathrm{i}}+12 \hat{\mathrm{k}}$


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