The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point?
The vector sum of the torques is zero. But the resultant force is not zero. The mathematical explanation is given as:
$G_{i} \sum_{i=1}^{n} F_{t} \neq 0$
$\tau=\tau_{1}+\tau_{2}+\ldots+\tau_{n}=\sum_{i=1}^{n} \underset{r_{i}}{\rightarrow} \times \overrightarrow{F_{i}}=0$
$\sum_{i_{1}}^{n}\left(\rightarrow_{r_{i}}-a\right) \times F_{t}=\sum_{i=1}^{n} \underset{r}{\rightarrow} \times F_{i}-a \sum_{i=1}^{n} F_{i}$
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