SOLUTION: Find the angle α between the vectors in radians a = (-2, 3), b = (6, 2)

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Question 1160830: Find the angle α between the vectors in radians
a = (-2, 3), b = (6, 2)

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
Cosine of the angle between the vectors "a" and "b" is equal to the scalar product of the vectors "a" and "b", 
divided by the product of their lengths


     = .


So, you have:  the scalar product is (-2)*6 + 3*2 = -12 + 6 = -6;

               |a| =  = ;

               |b| =  = .


Therefore,   =  =  = -0.26312.


So,   = arccos(-0.26312) = 1.837 radians.     ANSWER

Solved.

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If you want more explanation and/or an entire topic to learn from,  look into the lessons
    - Introduction to dot-product
    - Formula for Dot-product of vectors in a plane via the vectors components
    - Dot-product of vectors in a coordinate plane and the angle between two vectors
    - Perpendicular vectors in a coordinate plane
    - Solved problems on Dot-product of vectors and the angle between two vectors
    - Properties of Dot-product of vectors in a coordinate plane
    - The formula for the angle between two vectors and the formula for cosines of the difference of two angles

    - HOW TO find dot-product of two vectors in a plane
    - HOW TO find scalar product of two vectors in a coordinate plane
    - HOW TO find the angle between two vectors in a coordinate plane

For the full list of my lessons on dot-product with short annotations see the file  OVERVIEW of lessons on Dot-product.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Dot-product for vectors in a coordinate plane".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



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