Three students are pulling on a bag of skittles. Each applies a horizontal force. Student \( 1 \) pulls eastward with a force of \( 170 \) \( \text{N} \). Student \( 2 \) pulls southward with a force of \( 100 \) \( \text{N} \). Student \( 3 \) pulls with a force of \( 200 \) \( \text{N} \) at an angle of \( 20^{\circ} \) west of north. What is the net force exerted on the bag of skittles by the three students?