Parallelogram Law of Vectors (Alternate Method)

Recall,

If two vectors acting simultaneously at a point can be represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing through that point.

Figure 1 represents two vectors acting at a point O at an angle of θ with each other.

Complete the parallelogram by drawing DE parallel to OB and OD parallel to BE as shown in Figure 2 and join OE. OE represents the resultant vector R in magnitude and direction.

Let OB represent vector B and OD represent vector D.

∠O and ∠D are supplementarySupplementary angles are two angles whose sum is 180 degrees. More

∴ ∠O + ∠D = 180°

θ + ∠D = 180°

∠D = 180 - θ

Considering Figure 3 , the resultant can be found using the cosine rule;

R²