Direction Cosines/Angles and 3D Vectors

Rodrigo Pena

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Sep 30, 2021
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Hello, hope you are doing great !

I am looking for a formula that I can use to find the angle of a 3D vector projected on a plane. The only information that I have about this 3D vector are the direction angles or direction cosines. Please find enclosed pictures for better understanding.

YouTube Video Link: Direction Vector, Direction Angle, and Direction Cosine -- Relations in Vectors, 3D Space

In the end of the video this guy says that Cos(alpha), Cos(beta) and Cos(gamma) (direction cosines) are unit vectors of the 3D vector but it did not find the same result (71.06 deg).

Thanks in Advance.
 

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