A pilot flies a plane at a speed of 600 km/h with respect to the surrounding air. A wind is blowing to the northeast at a speed of 100 km/h. In what direction must the plane be aimed so that the resulting direction of the plane is due north?

Answer 1

Graphically this is so easy, and that is exactly how pilots would do it.
Put the wind at 100 NE, then on the end of that, take a vector from that point 600 in length, use a compass to draw an arc until it intercepts N. Then that is the direction.

Want to do it analytically?

You have the wind giving a 70.7km/h push to the East, so the plane must cancel that with a 70.7 W component.

so 70.7=600sinTheta (theta measured from N).
sinTheta= 70.7/600
theta= aresin (above) WEST of N