Finding the angle of 3-dimensional vectors.

[niyati]

How would the angle between two vectors be found, if, for each vector, three components (i, j, k) were given?

Ex. Given that vector A = 2.0 i + 4.0 j - 7.0 k and vector B = 5.0 i - 3.0 j + 1.0 k, what is the angle between A and B?

 

[neutrino]

Use the definition of the scalar (dot) product.

 

[FedEx]

Ok.

We can find it by dot product.We know that for two vectors A and B

$$\vec{A} \cdot \vec{B} = AB\cos\theta$$

Hence find A dot B and divide it by AB. And take its arccosine and you will get your angle.

 

[niyati]

...dot...product?

All right. I'm pulling out some of my old Pre-Cal stuff, when I learned that. D

Thank you.