Following sets of three forces act on a body. Whose resultant cannot be zero
$10, 10, 10$
$10, 10, 20$
$10, 20, 23$
$10, 20, 40$
Statement $I:$ If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}$, then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement $II:$ A triangle made up of three forces $\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}$ and $\overrightarrow{{F}}_{3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:
Two forces are such that the sum of their magnitudes is $18\; N$ and their resultant is $12\; N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are
Which of the following is independent of the choice of co-ordinate system