What is the resultant velocity for a plane that is flying due east at 33m/s that is also being carried due north at 12m/s by the wind

  v = 35.11 m / s,    θ = 20º    north of east

Explanation:

This is a compound problem of relative velocities, we can use the Pythagorean theorem to find the modulus of the resulting velocity

            v² = v₁² + v₂²

where the eastward velocity is v₁=33 m/s and the northward velocity

v₂=12 m / s

            v =

             v = 35.11 m / s

the direction of this velocity can be found with the uses of trigonometry

           tan θ = v₂ / v₁

           θ = tan⁻¹ v₂ / v₁

           θ = tan⁻¹ 12/33

           θ = 20º

this angles is north of east

whichever one it is, it's definitely not one that you included on the list you provided.

this a false

explanation: