the conditions that the net force and the net torque both vanish?

Answer 1

for a body to be in equillibrium, exist two condition:

The sum total of forces in the space vectorial must be zero
sum of forces en x equal zero
sum of forces en y equal zero
sum of forces en z equal zero

and the other condition is:

The sum total of torque in the space vectorial must be zero
sum of torque en x equal zero
sum of torque en y equal zero
sum of torque en z equal zero

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