Calculating Angle Between Vectors Using Cosine Law

In summary, the conversation is about someone seeking help to solve a problem involving the addition of two displacements. They are looking for an explanation and not just the answer. The problem involves finding the angle between two displacements to get a resultant displacement of different magnitudes. The cosine law is mentioned as a helpful formula for solving the problem.
  • #1
Uira
1
0
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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  • #2
This is referring to addition of the displacements.

You have a triangle, and know the lengths of the 3 sides. Find the angle/s.
 
  • #3
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]
 

FAQ: Calculating Angle Between Vectors Using Cosine Law

What is the angle between two vectors?

The angle between two vectors is the measure of the amount of rotation needed to align one vector with the other. It is usually measured in degrees or radians.

How do you calculate the angle between two vectors?

The angle between two vectors can be calculated using the dot product or the cross product of the two vectors. The formula for calculating the angle using the dot product is:
θ = cos-1 (a·b / |a||b|), where a and b are the two vectors. The formula using the cross product is: θ = sin-1 (|a×b| / |a||b|).

What is the range of possible values for the angle between two vectors?

The range of possible values for the angle between two vectors is 0° to 180°. If the vectors are parallel, the angle is 0°, and if they are anti-parallel, the angle is 180°. If the vectors are perpendicular, the angle is 90°.

How does the direction of the vectors affect the angle between them?

The direction of the vectors does not affect the angle between them. The angle between two vectors is only dependent on their magnitudes and the angle between their directions. It is the same whether the vectors are pointing in the same or opposite directions.

What is the difference between acute, obtuse, and right angles between two vectors?

An acute angle between two vectors is less than 90°, an obtuse angle is greater than 90°, and a right angle is exactly 90°. These types of angles can be formed between any two vectors, depending on their directions and magnitudes.

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