Lesson 1, Topic 3
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# Parallelogram Law of Vectors (Alternate Method)

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### 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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#### Responses

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

1. 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}