document.write( "Question 1187474: 1. Find vectors ~v and ~w such that ~v is parallel to ~u = 2~ı − 3~j, ~w is perpendicular to ~u and ~v + ~w = 4~ı + 4~j. (The signs \"~\" are arrows that go above)\r
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Algebra.Com's Answer #819454 by math_helper(2461) $\"\"$ $\"About$

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document.write( "I will use bold v, u, and w to denote vectors, and
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document.write( "notation like  to denote components of a vector (here x component of vector u)  \r
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document.write( "Hopefully it renders properly.\r
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document.write( "u = 2i - 3j           (1)\r
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document.write( "From v || u: v = 2ci-3cj   (2)
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document.write( "   where  c  is some scaler value.\r
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document.write( "From w perpendicular to u:  w∙u = 0
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document.write( "   which translates to
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document.write( "         2 - 3 = 0     (3)\r
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document.write( "We also want:  w + v = 4i + 4j    (4) \r
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document.write( "(3) ==>  \r
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document.write( "Now we can write, using (3) and (4):
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document.write( " (5)   2c +  = 4
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document.write( " {6)  -3c +  = 4\r
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document.write( "Solving this for c gives    which tells us via (2)
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document.write( "that v = (-8/13)i + (12/13)j\r
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document.write( "Now you can use (5) and (6) to solve for  or plug  c into 
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document.write( "(4) and solve for  and  (I did it the latter way):\r
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document.write( " w = (60/13)i + (40/13)j\r
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document.write( "Check:
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document.write( "I checked everything but you should do so as an exercise.
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document.write( "1.  Check that w + v = 4i + 4j
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document.write( "2.  Check that w∙u = 0  ()
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document.write( "3.  Check that |v∙u| = |v||u|\r
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