In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the day, and she is blown along the following straight lines: 3.00 km and 45.0\north of west, then 5.90 km and 60.0\$^\circ$ south of east, then 2.80 km and 25.0\$^\circ$ south of west, then 5.10 km due east, then 1.70 km and 6.00\$^\circ$ east of north, then 7.20 km and 55.0\$^\circ$ south of west, and\finally 2.80 km and 10.0\$^\circ$ north of east. Use the analytical method to find the resultant vector of all her displacement vectors (in m). (Express your answer in vector form. Assume the $+x$-axis is to the\east and the $+y$-axis is to the north.)
What is its magnitude (in km) and direction (in degrees south of east)?
magnitude
km
direction
$^\circ$ south of east