1. Adding Vectors
Example of adding two vectors neither at right angles to one another nor on an x or y axis.

2. The Process:
First draw the vectors on an x:y axis, showing them attached head to tail.
Second, determine the x and y components of V1.
Third, determine the x and y components of V2.
Fourth, Add the x components of the vectors together.
Fifth, Add the y components of the vectors together.
Sixth, Use the sum of the x components as the x component of the resultant vector; Use the sum of the y components as the y component of the resultant vector.
Seventh, proceed to “add” the resultant’s x and y values.

3. The Problem:

4. Resolve the 1st vector into its x and y components.
V1y = V1 * Sin 60 or V1 * Cos 30 = Km, N
V1x = V1 * Cos 60 or V1 * Sin 30 = 0.5 km, E

5. Resolve the 2nd vector into its x and y components.
V2y = V2 * Sin 30 or V2 * Cos 60 = 1 Km, N
V2x = V2 * Cos 30 or V2 * Sin 60 = Km, E

6. Next, add the components.
V1y + V2y = Km Km = Km, N
V1x + V2x = Km Km = Km, E

7. Determine the resultant:
1st use c^2 = a^2 + b^2
c = (a^2 + b^2)^(1/2)
c = [(1.866 km)^2 + (2.232 km)^2]^(1/2)
So c = km
2nd use Angle = Inv Tan (Ry / Rx) = Inv Tan (1.886 km / km) = 39.9 degrees; The direction is N of E.
So R (the resultant) is equal to Km, 39.9 deg N of E
or Km, 50.1 deg from N, or E of N