# How to calculate Angle between vectors

1. Dec 6, 2007

### IMK

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.

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• ###### vectors.GIF
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Last edited: Dec 6, 2007
2. Dec 6, 2007

### HallsofIvy

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. Dec 6, 2007

### IMK

These would be force vectors that I would normalize to be in the range of 0 to 1

4. Dec 6, 2007

### nicksauce

$$\vec{A}\cdot\vec{B}= \|\vec{A}\|\|\vec{B}\|\cos{\theta}$$ and
$$\|\vec{A}\times\vec{B}\|=\|\vec{A}\|\vec{B}\|\sin{\theta}$$. You can use either of these to calculate the angle.

5. Dec 6, 2007

Many thanks!