Calculating Angle Between Vectors Using Cosine Law

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SUMMARY

The discussion focuses on calculating the angle between two vectors using the cosine law. The problem involves two displacements with magnitudes of 2.6 and 3.9, and the goal is to determine the angles that yield resultant displacements of 5.7m, 2.6m, and 3.2m. The cosine law formula, c² = a² + b² - 2ab cos(C), is essential for solving this problem. Participants emphasize the importance of understanding the derivation and application of the cosine law in vector addition.

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  • Understanding of vector addition
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  • Basic knowledge of triangle properties
  • Ability to manipulate algebraic equations
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  • Explore applications of the cosine law in physics and engineering
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Hello, I've been trying to solve this problem for hours now, but i keep getting it wrong. Been looking for examples but i don't seem to find one with a good explanation, so any help is appreciated.

The problem:

Consider two displacements, one of magnitude 2.6 and another of magnitude 3.9. What angle between the directions of these two displacements give a resultant displacement of magnitude a) 5.7m b)2.6m c)3.2

If anyone can please help me understand, thank you. Please, don't just post the answer, i want to learn how to solve it.
 
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This is referring to addition of the displacements.

You have a triangle, and know the lengths of the 3 sides. Find the angle/s.
 
A formula that will help is the cosine law. If a triangle has sides a, b, and c and C is the angle opposite side c, then [itex]c^2= a^2+ b^2- 2ab cos(C)[/itex]
 

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