With the diagram and the data answer the question: What is the magnitude of A + B?
Using the provided diagram and data, please answer the following question: What is the magnitude of A + B?
Diagram: http://i43.tinypic.com/1e9ik6.jpg
Data: θ1 = 40.1°, θ2 = 132.7°, A = 5.9 cm, B = 8.3 cm.
1 Answers
A and B are vector Quantities.
The angle between vector A and vector B = 180 - (θ2 - θ1)
[Do not be confused that the angle between A and B is (θ2 - θ1)]
By Cosine Law of Vector Addition,
Vector(A + B)
= √{ A² + B² - 2AB cos(180 - (θ2 - θ1)) }
= √{ A² + B² + 2AB cos(θ2 - θ1) }
Putting the Corresponding Values,
= √{ (5.9)² + (8.3)² + 2(5.9)(8.3) cos(132.7° - 40.1°) }
= 9.963 cm
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