document.write( "Question 1117162: Given that a = 5i + 9j - 2k and b = -3i - 7j + 4k, find the direction cosines and a unit vector in the direction of 6a + 3b. \n" ); document.write( "

Algebra.Com's Answer #732196 by Fombitz(32388) $\"\"$ $\"About$

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a=(5,9,-2)
\n" ); document.write( "6a=(30,54,-12)
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\n" ); document.write( "b=(-3,-7,4)
\n" ); document.write( "3b=(-9,-21,12)
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\n" ); document.write( "c=6a+3b=(30-9,54-21,-12+12)=(21,33,0)
\n" ); document.write( " $\"abs%28c%29=sqrt%2821%5E2%2B33%5E2%29=sqrt%281530%29=3sqrt%28170%29\"$
\n" ); document.write( "The direction cosines are then,
\n" ); document.write( " $\"alpha=21%2F%283sqrt%28170%29%29=7%2Fsqrt%28170%29=%287%2F170%29sqrt%28170%29\"$
\n" ); document.write( " $\"beta=33%2F%283sqrt%28170%29%29=11%2Fsqrt%28170%29=%2811%2F170%29sqrt%28170%29\"$
\n" ); document.write( " $\"delta=0%2F%283sqrt%28170%29%29=0\"$ \r
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