Question 1160830
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<pre>
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


    {{{cos(alpha)}}} = {{{(a*b)/(abs(a)*abs(b))}}}.


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

               |a| = {{{sqrt((-2)^2+3^2)}}} = {{{sqrt(13)}}};

               |b| = {{{sqrt(6^2+2^2)}}} = {{{sqrt(40)}}}.


Therefore,  {{{cos(alpha)}}} = {{{-6/(sqrt(13)*sqrt(40))}}} = {{{-3/(sqrt(13)*sqrt(10))}}} = -0.26312.


So,  {{{alpha}}} = arccos(-0.26312) = 1.837 radians.     <U>ANSWER</U>
</pre>

Solved.


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If you want more explanation and/or an entire topic to learn from, &nbsp;look into the lessons

&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/Perpendicular-vectors-in-a-coordinate-plane.lesson>Perpendicular vectors in a coordinate plane</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/Vectors/Properties-of-Dot-product-of-vectors-in-a-coordinate-plane.lesson>Properties of Dot-product of vectors in a coordinate plane</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/The-formula-for-the-angle-between-two-vectors-and-the-formula-of-cosines-of-the-difference-of-two-angles.lesson>The formula for the angle between two vectors and the formula for cosines of the difference of two angles</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>


For the full list of my lessons on dot-product with short annotations see the file &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Vectors/REVIEW-of-the-lessons-on-Dot-product.lesson>OVERVIEW of lessons on Dot-product</A>. 


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 &nbsp;"<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.