Two unit vectors x and y in RR^n satisfy x * y=2sqrt(2) in radians. How would I go about finding the angle between x and y?

Ibrahim Rosales

Ibrahim Rosales

Answered question

2022-07-21

Two unit vectors x and y in R n satisfy x y = 2 2 in radians. How would I go about finding the angle between x and y?
As I don't know the x and y unit vectors, would the unit circle be useful here? For instance, using 2 2 and plugging those values into x y x y to find the angle?

Answer & Explanation

Sheldon Castillo

Sheldon Castillo

Beginner2022-07-22Added 10 answers

No, I believe the unit circle is not really involved here.
It is simple. You already know the cosinus of the angle θ between the two vectors. It is this expression:
c o s ( θ ) = x y | | x | | | | y | |
Just plug in the numbers in this formula. Thus you get:
c o s ( θ ) = 2 / 2 1.1
And once you know that a = c o s ( θ ) = 2 / 2
find θ = arccos ( a ) = arccos ( 2 / 2 ) = π / 4
Mariah Sparks

Mariah Sparks

Beginner2022-07-23Added 3 answers

The dotproduct between two vectors in euclidean space can be defined as
x y = cos θ | | x | | | | y | |
Since you have unit vectors: | | x | | , | | y | | = 1. The angle θ is then given by
θ = arccos ( x y ) = arccos ( 2 / 2 ) = π / 4

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