Atypical way to find angle between unit vectors: \theta =

Jayleen Sanders

Jayleen Sanders

Answered question

2022-01-29

Atypical way to find angle between unit vectors: θ=2sin1(12|A^B^|)
At my work, I have come across code with the following way of calculating the angle between two vectors.
θ=2sin1(12|A^B^|)
(Note the physics convention: v^ indicates the normalization of v; ie, v^=v|v|).

Answer & Explanation

stamptsk

stamptsk

Beginner2022-01-30Added 23 answers

This works when A and B are unit vectors.
You have
|AB|2=(AB)(AB)=|A|2+|B|22,AB=22cosθ=4sin2θ2
Solving,
θ=2arcsint|AB|2

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