To find the vector that is equivalent to a vector of 12 Newtons at 75 degrees south of west, we need to determine the direction and magnitude of the equivalent vector.
The equivalent vector will have the same magnitude of 12 Newtons but a direction that is 180 degrees opposite to the given vector.
The given vector is 75 degrees south of west, which means it is pointing towards the south but slightly to the west.
Therefore, the direction of the equivalent vector will be 75 degrees north of east (opposite direction).
Among the given options:
a) 12 N at 15 degrees west of south - This is not the correct direction.
b) 12 N at 15 degrees south of east - This is not the correct direction.
c) 12 N at 15 degrees north of east - This is the correct direction.
d) 12 N at 15 degrees south of west - This is not the correct direction.
Therefore, the vector that is equivalent to the given vector is option c) 12 N at 15 degrees north of east.