Question 1173623
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You just got two solutions from Edwin,  and you,  probably,  have a question,  which approach/method to prefer.



Of these two approaches,  the method using cosine is  ROBUST  and works  ALWAYS,  and  ALWAYS  produces correct results.



The Edwin's formulas with tan and arctan have a huge underwater stone.



In this form, as they presented,  they work and they produce a correct answer for an  ACUTE  angle,  ONLY.



For an  OBTUSE  angle they do not work.



AGAIN:   the method using cosine and scalar products,  is  ROBUST  and  STANDARD  method for such problems.



For them,  use it and  ONLY  it . . . 


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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Introduction-to-dot-product.lesson>Introduction to dot-product</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Formula-for-Dot-product-of-vectors-in-a-plane-via-the-vectors-components.lesson>Formula for Dot-product of vectors in a plane via the vectors components</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Dot-product-of-vectors-in-a-plane-and-the-angle-between-two-vectors.lesson>Dot-product of vectors in a coordinate plane and the angle between two vectors</A> (*)

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Solved-problems-on-Dot-product-of-vectors-and-the-angle-between-two-vectors.lesson>Solved problems on Dot-product of vectors and the angle between two vectors</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-find-dot-product-of-two-vectors-in-a-plane.lesson>HOW TO find dot-product of two vectors in a plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-find-scalar-product-of-two-vectors-in-a-coordinate-plane.lesson>HOW TO find scalar product of two vectors in a coordinate plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-find-the-angle-between-two-vectors-in-a-coordinate-plane.lesson>HOW TO find the angle between two vectors in a coordinate plane</A>



Of these lessons, the key is the lesson marked (*) in the list.

It is the most relevant lesson to your problem.


Other lessons illustrate how everything work.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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



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.