What is the Law of Cosines for Calculating Vector Magnitudes?

In summary, the problem involves two vectors ~A and ~B with magnitudes of 12.1 and 7 respectively, acting at 130 degrees to each other. The task is to use the law of cosines to calculate the magnitude of the resultant vector ~A + ~B. This is done by drawing a triangle and using the equation (A+B)^2 = A^2 + B^2 - 2ABcosθ, where θ is the angle between the two vectors. The correct angle to use is not 130 degrees, but rather the angle between the two vectors when drawn "tip-to-tail". This results in a calculated magnitude of 17.444148.
  • #1
Andy111
26
0

Homework Statement



Consider two vectors ~A and ~B and their resul-
tant ~A + ~B . The magnitudes of the vectors ~A
and ~B are, respectively, 12.1 and 7 and they
act at 130◦ to each other.

Use the law of cosines to calculate the mag-
nitude of the resultant vector ~A + ~B.

Homework Equations





The Attempt at a Solution

 
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  • #2
Andy111 said:

Homework Statement



Consider two vectors ~A and ~B and their resul-
tant ~A + ~B . The magnitudes of the vectors ~A
and ~B are, respectively, 12.1 and 7 and they
act at 130◦ to each other.

Use the law of cosines to calculate the mag-
nitude of the resultant vector ~A + ~B.

Homework Equations


The Attempt at a Solution


How do you figure to apply the Law of Cosines?
 
  • #3
I did (A+B)[tex]^{2}[/tex]=A[tex]^{2}[/tex]+B[tex]^{2}[/tex]-2ABcos(130) and solved for (A+B). I got an answer of 17.444148, but that was wrong.
 
  • #4
Draw a triangle using those vectors.

edit:
This will show you the angle you are supposed to use for the calculation.
 
  • #5
I'm a bit lost, why isn't 130 the correct angle to use?
 
  • #6
Did you draw the triangle?

A picture is worth 1000 words.
 
  • #7
Well yes, and I put the angle 130 between A and B, and if that's correct then I don't know how I got this wrong.
 
  • #8
The correct picture is the 2nd one here.
 

Attachments

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  • #9
Thanks, I see where my mistake was now, I didn't draw the vectors "tip-to-tail".
 

What is a vector calculation problem?

A vector calculation problem is a mathematical problem that involves the use of vectors, which are quantities that have a magnitude and direction. These problems usually require the use of vector addition, subtraction, and multiplication to find a solution.

What are some common applications of vector calculation problems?

Vector calculation problems are commonly used in physics, engineering, and computer graphics to solve problems related to motion, forces, and other physical phenomena. They are also used in navigation, such as finding the direction and magnitude of a plane's velocity.

What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature and time, while examples of vectors include displacement and velocity.

How do you find the magnitude of a vector?

The magnitude of a vector is found by taking the square root of the sum of the squared components of the vector. It is often denoted by ||v||, where v represents the vector.

What is the difference between vector addition and vector subtraction?

Vector addition involves combining two or more vectors to find their resultant, while vector subtraction involves finding the difference between two vectors. Both operations can be performed by adding or subtracting the components of the vectors in the same direction.

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