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How to Find the Angle Between Two Vectors: 3 Steps

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How to Find the Angle Between Two Vectors

The angle between two vectors is called the shortest angle at which you have to turn around one of the vectors to the position of co-directional with another vector. There are three steps for finding it:

The first step is to calculate dot product of vectors. It is also called scalar product or inner product. From geometrical point it’s also the product of magnitudes of vectors multiplied by the cosine of the angle between vectors.
There is a special formula for finding dot product 01:13.
Shortly:
1) Multiply the first coordinates of the vectors
2) Multiply the second coordinates of the vectors
3) Add the resulting values

The second step is to calculate vectors magnitude. Or the length of the vector in other words 02:33. It can be found using the following actions:
1) Square each vector's coordinate
2) Add them together
3) Extract a square from the sum
Once you got it, you can move to the last step.

The third step is to calculate the cosine of the angle between the two vectors 03:09. When you have got the cosine you can find the angle. For that you should use a special table of cosines. Got it?

Yep, math is quite abstract. To help you understand it better we use simple example 03:17. Even kids are able to manage!

Hope you too can use this instruction easily. Stay with us!

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