document.write( "Question 1173622: u = −10i − 5j
\n" ); document.write( "v = −6i + 3j\r
\n" ); document.write( "\n" ); document.write( "Find the degree measure of the angle 𝜃 between the vectors. (Round your answer to two decimal places.)\r
\n" ); document.write( "\n" ); document.write( "𝜃 = _____°
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Algebra.Com's Answer #798899 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "The dot product of two vectors is defined as\r
\n" ); document.write( "\n" ); document.write( "u·v = |u||v|cos(θ)\r
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\n" ); document.write( "\n" ); document.write( "and the dot product also happens to be the sum of products of corresponding components:\r
\n" ); document.write( "\n" ); document.write( "u·v = \"u%5Bx%5Dv%5Bx%5D+%2B+u%5By%5Dv%5By%5D\" \r
\n" ); document.write( "\n" ); document.write( "So we have all that is needed to solve for θ:\r
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\n" ); document.write( "\n" ); document.write( "|u| = \"+sqrt%28%28-10%29%5E2+%2B+%28-5%29%5E2%29+\" = \"+sqrt%28125%29+\" = \"+5sqrt%285%29+\"
\n" ); document.write( "|v| = \"+sqrt%28%28-6%29%5E2+%2B+3%5E2%29+\" = \"+sqrt%2845%29+\" = \"+3sqrt%285%29+\"\r
\n" ); document.write( "\n" ); document.write( "and
\n" ); document.write( "\"+u%5Bx%5Dv%5Bx%5D+%2B+u%5By%5Dv%5By%5D\" = \"+%28-10%29%28-6%29+%2B+%28-5%29%283%29+\" = \"+45+\"\r
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\n" ); document.write( "\n" ); document.write( "Putting it all together:\r
\n" ); document.write( "\n" ); document.write( " \"5sqrt%285%29%2A3sqrt%285%29%2Acos%28theta%29+\" = \"45+\"
\n" ); document.write( " \"75+cos%28theta%29+\" = \"45+\"
\n" ); document.write( " cos(θ) = \"45%2F75+\" \r
\n" ); document.write( "\n" ); document.write( " θ = \"cos%5E-1%2845%2F75%29+\" = \"highlight%28+53.13%5Eo+%29+\"
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