Question 1075779
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<pre>
The dot product of these vectors is U*V = 7*0 + 2*(-4) = 0 - 8.


The length of the vector U is |U| = {{{sqrt(7^2 + 2^2)}}} = {{{sqrt(53)}}}.


The length of the vector V is |V| = {{{sqrt((-4)^2)}}} = {{{sqrt(16)}}} = 4.


Then the cosine of the angle between the vectors U and V is 


{{{cos(alpha)}}} = {{{(U*V)/(abs(U)*abs(V))}}} = {{{-8/(4*sqrt(53))}}} = {{{-2/sqrt(53)}}}. 


Hence, {{{alpha}}} = {{{arccos(-2/sqrt(53))}}}.


Please complete calculations on your own from this point.
</pre>

There are lessons on dot-product in this site that can be useful to you:

&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>



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>".