Question 1117162
a=(5,9,-2)
6a=(30,54,-12)
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b=(-3,-7,4)
3b=(-9,-21,12)
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c=6a+3b=(30-9,54-21,-12+12)=(21,33,0)
{{{abs(c)=sqrt(21^2+33^2)=sqrt(1530)=3sqrt(170)}}}
The direction cosines are then,
{{{alpha=21/(3sqrt(170))=7/sqrt(170)=(7/170)sqrt(170)}}}
{{{beta=33/(3sqrt(170))=11/sqrt(170)=(11/170)sqrt(170)}}}
{{{delta=0/(3sqrt(170))=0}}}