Aplane flies with a velocity of 52m/s east through a 12 m/s cross wind blowing from the north. find the resultant velocity

From a bird's eye view, the plane will be flying northeast.  The velocity in the direction of flight will be slightly more than 52m/s; it will be the length of the hypotenuse of the right triangle formed by it's east and north velocities.

Its east velocity is 52m/s and its north velocity is 12m/s so its velocity from a bird's eye view is (by the Pythagorean theorem)