There are 2 ways to do this...neither is easier than the other.
Draw a figure in any case....a parallelogram of which you need to find the direction of the shorter diagonal.
NW is 45° counterclockwise from N. which tells you the smaller angle of the parallelogram is 45°
Method I
The magnitude of the resultant vector is given by the law of cosines
r=sqrt(36+169-2 *6*13 cos 45°)
Then the direction will be given by the law of sines:(r/sin 45°)=13/sin x) where x is the angle you want in degrees.
Method 2
The other is to recognize that the point of the east going vector is (6,0) and the NW vector tip is
(-6.5√2,6.5√2) because the sides of an isosceles right triangle are obtained as the hypotenuse times (1/2) sqrt(2).
The tip of the resultant vector is obtained by adding the co-ordinates.
Then the tangent of the direction will be given as y/x from the tip you got by adding.
