document.write( "Question 1160830: Find the angle α between the vectors in radians
\n" ); document.write( "a = (-2, 3), b = (6, 2) \n" ); document.write( "

Algebra.Com's Answer #784246 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Cosine of the angle between the vectors \"a\" and \"b\" is equal to the scalar product of the vectors \"a\" and \"b\", \r\n" );
document.write( "divided by the product of their lengths\r\n" );
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document.write( "     = .\r\n" );
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document.write( "So, you have:  the scalar product is (-2)*6 + 3*2 = -12 + 6 = -6;\r\n" );
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document.write( "               |a| =  = ;\r\n" );
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document.write( "               |b| =  = .\r\n" );
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document.write( "Therefore,   =  =  = -0.26312.\r\n" );
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document.write( "So,   = arccos(-0.26312) = 1.837 radians.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want more explanation and/or an entire topic to learn from, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to dot-product\r
\n" ); document.write( "\n" ); document.write( "    - Formula for Dot-product of vectors in a plane via the vectors components\r
\n" ); document.write( "\n" ); document.write( "    - Dot-product of vectors in a coordinate plane and the angle between two vectors\r
\n" ); document.write( "\n" ); document.write( "    - Perpendicular vectors in a coordinate plane\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Dot-product of vectors and the angle between two vectors \r
\n" ); document.write( "\n" ); document.write( "    - Properties of Dot-product of vectors in a coordinate plane \r
\n" ); document.write( "\n" ); document.write( "    - The formula for the angle between two vectors and the formula for cosines of the difference of two angles\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO find dot-product of two vectors in a plane\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO find scalar product of two vectors in a coordinate plane\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO find the angle between two vectors in a coordinate plane\r
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\n" ); document.write( "\n" ); document.write( "For the full list of my lessons on dot-product with short annotations see the file OVERVIEW of lessons on Dot-product. \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Dot-product for vectors in a coordinate plane\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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