How to calculate Angle between vectors

In summary, the conversation is about calculating the angle between three force vectors represented by black lines, as well as the angle between any of those vectors and a central red vector. The process for calculating the angle depends on how the vectors are given, but they can be normalized to a range of 0 to 1 and then used in equations involving the dot product and cross product.
  • #1
IMK
63
0
Hello,
In attached image the three black lines represent three force vectors x,y,z of some arbitrary magnitude, these I can normalize and by taking the sin-1 I get there effect angle. What I would like to calculate is the angle between any two of the black line axies thus theta xy = ?. also I would like to calculate the angle between any of the x,y,z axies and the and the central red vector.

Many thanks in advance IMK
 

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  • #2
In order to "calculate" the angle (as opposed to measuring it) you have to be "given" the vectors in some "calculable" form. How you would then calculate the angle depends on how you are given the vectors. How are you given x, y, and z, other than just a drawing?
 
  • #3
HallsofIvy said:
In order to "calculate" the angle (as opposed to measuring it) you have to be "given" the vectors in some "calculable" form. How you would then calculate the angle depends on how you are given the vectors. How are you given x, y, and z, other than just a drawing?

These would be force vectors that I would normalize to be in the range of 0 to 1
Many thanks in advance IMK
 
  • #4
[tex]\vec{A}\cdot\vec{B}= \|\vec{A}\|\|\vec{B}\|\cos{\theta}[/tex] and
[tex]\|\vec{A}\times\vec{B}\|=\|\vec{A}\|\vec{B}\|\sin{\theta}[/tex]. You can use either of these to calculate the angle.
 
  • #5
nicksauce said:
[tex]\vec{A}\cdot\vec{B}= \|\vec{A}\|\|\vec{B}\|\cos{\theta}[/tex] and
[tex]\|\vec{A}\times\vec{B}\|=\|\vec{A}\|\vec{B}\|\sin{\theta}[/tex]. You can use either of these to calculate the angle.
Many thanks!
 

FAQ: How to calculate Angle between vectors

1. What is the formula for calculating the angle between two vectors?

The formula for calculating the angle between two vectors is:

θ = cos^-1((a · b) / (|a| * |b|))

2. How do I find the magnitude of a vector?

The magnitude of a vector can be found by taking the square root of the sum of its squared components.

|a| = √(a1^2 + a2^2 + a3^2)

3. Can the angle between two vectors be negative?

No, the angle between two vectors is always a positive value. If the vectors are pointing in opposite directions, the angle will be 180 degrees or π radians.

4. What is the unit of measurement for the angle between vectors?

The unit of measurement for the angle between vectors is radians.

5. How do I calculate the angle between vectors in 3-dimensional space?

To calculate the angle between vectors in 3-dimensional space, you can use the same formula as in 2-dimensional space. However, you will need to use the dot product of the two vectors, which includes the third component.

θ = cos^-1((a1 * b1 + a2 * b2 + a3 * b3) / (|a| * |b|))

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