# Vectors finding direction include the difference between “north of east” and “east of north”

In what direction is your friend from the starting point after skiing 3 km east and then 1.5 km north?

so far I know that angle= tan-1(opp/adj)=(1.5/3.0) angle= 26.6degrees now if i say that the final location is 26.6 degrees north of east is that correct?

an i state the answer by saying east of north would that be: 90- 26.6=63.4 is it always the case that north of east implies counter-clock wise and east of northimply clockwise?

• Yes that sounds right. Draw yourself a diagram. A picture is worth more than words. Incidentally the compass rose is divided into 360 degrees with North being zero, East being 90, etc. that give you another way of describing the answer. – Floris Feb 6 '16 at 4:48

1. By convention, North and South rank higher in the English language. Thus we have Northeast and not Eastnorth.
2. You have presumed a flat earth. If you start 1.5 km from the North Pole, then after skiing 3 km east and 1.5 km north, you will be at the North Pole, 1.5 km North from your starting point.
• 100% of mathematicians and scientists live more than 1.5km from the north pole, and most of them live a rather large distance from either pole, so I don't think your second point is relevant per se. – Asher Feb 6 '16 at 5:06
• 2nd point is irrelevant and also not clear. – Anubhav Goel Feb 6 '16 at 5:38