document.write( "Question 939326: Here is my problem, concerning vectors and norms(?)
\n" ); document.write( "I have the following information:
\n" ); document.write( "u and v are two vectors.
\n" ); document.write( "|| u || = 3, || v || = sqrt(5), and u·v = 1 [dot product]. With this information, find
\n" ); document.write( "|| u + v || = ?\r
\n" ); document.write( "\n" ); document.write( "I know from proofs that it is impossible for || u + v || to be larger than ||u|| + ||v||, but I cannot seem to get the answer for the life of me.\r
\n" ); document.write( "\n" ); document.write( "The answer (since this was a practice problem) is 4, and I'd love to know the \"how\".\r
\n" ); document.write( "\n" ); document.write( "Thanks! \n" ); document.write( "
Algebra.Com's Answer #572337 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Hint: Draw the two vectors where their tails start at the same point. The first vector u is in black while the other vector v is in blue. The angle between the two vectors is shown in purple the angle \"alpha\". Use the parallelogram rule to help you construct the red resultant vector \"u%2Bv\"\r
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\n" ); document.write( "\n" ); document.write( "You can use the formula \"cos%28alpha%29+=+%28u%2Av%29%2F%28abs%28u%29%2Aabs%28v%29%29\" to find the angle \"alpha\". Note: u and v are vectors, so when I say \"u%2Av\" I mean \"dot product of u and v\".\r
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\n" ); document.write( "\n" ); document.write( "We're dealing with a parallelogram. So the adjacent angles are supplementary meaning that \"alpha+%2B+theta+=+180\". Use the value of alpha to find theta.\r
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\n" ); document.write( "\n" ); document.write( "Once you know theta, you can then use the law of cosines \"c%5E2+=+a%5E2%2Bb%5E2+-2ab%2Acos%28C%29\" to find the length of the red resultant vector which will be your answer. \n" ); document.write( "
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