### Topic Content:

- 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 Î¸ 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.

âˆ O and âˆ D are supplementary

âˆ´ âˆ O + âˆ D = 180Â°

Î¸ + âˆ D = 180Â°

âˆ D = 180 – Î¸

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

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In the second question, the resultant vector should be 28N. Why use 35N as the resultant in your solution

We are looking for angle x. The cosine rule is a general rule and uses the side facing the angle, which in this case is 35 N. So in this case c = 35 N, a = 15, b = 28 and angle = x. cosine rule = c = \sqrt{a^2 + b^2 – 2ab cos x}