document.write( "Question 1193904: Let u=−3i+j+k and v=mj+nk, where m, n∈ . Given that v is a unit vector perpendicular to u, find the possible values of m and of n. \n" ); document.write( "

Algebra.Com's Answer #825953 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "Let u=−3i+j+k and v=mj+nk, where m, n∈ .
\n" ); document.write( "Given that v is a unit vector perpendicular to u, find the possible values of m and of n.
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document.write( "Since vectors u and v are perpendicular, their scalar product is zero.\r\n" );
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document.write( "It gives first equation\r\n" );
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document.write( "    m + n = 0.         (1)\r\n" );
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document.write( "Since vector v has the length of 1, it gives you second equation\r\n" );
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document.write( "    m^2 + n^2 = 1.     (2)\r\n" );
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document.write( "From (1), express  m = -n and substitute into (2). You will get\r\n" );
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document.write( "    (-n)^2 + n^2 = 1\r\n" );
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document.write( "          2n^2   = 1\r\n" );
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document.write( "           n = +/- .\r\n" );
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document.write( "ANSWER.   There are two possibilities:\r\n" );
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document.write( "          (a)  m = ,  n = -,\r\n" );
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document.write( "    and/or\r\n" );
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document.write( "          (b)  m = -,  n = .\r\n" );
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