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 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 supplementary
∴ ∠O + ∠D = 180°
θ + ∠D = 180°
∠D = 180 – θ
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}