Question

A Force F=3i-4j+12k act at a point whose coordinates are (1,-2,3)m. The moment of force about the origin would be?​

Answer 1

moment of force means, torque.

indirectly, question said to find torque of the point about origin.

we know, torque is the cross product of position vector and force vector.

e.g., $\tau=\vec{r}\times\vec{F}$

position vector , $\vec{r}$ = i - 2j + 3k

force vector, $\vec{F}$ = 3i - 4j + 12k

now, torque , $\tau$ = (i - 2j + 3k) × (3i - 4j + 12k)

= $\left|\begin{array}{ccc}i&j&k\\1&-2&3\\3&-4&12\end{array}\right|$

= i(-2 × 12 - 3 × -4) -j(1 × 12 - 3 × 3) + k{1 × -4 - (-2) × 3}

= i(-24 + 12) -j(12 - 9) + k(-4 + 6)

= -12i - 3j + 2k

hence, torque of the point about origin is (-12i - 3j + 2k) Nm.

or, the moment of the point about origin would be (-12i - 3j + 2k)