SOLUTION: 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.

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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.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a=(5,9,-2)
6a=(30,54,-12)
.
.
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%28c%29=sqrt%2821%5E2%2B33%5E2%29=sqrt%281530%29=3sqrt%28170%29
The direction cosines are then,
alpha=21%2F%283sqrt%28170%29%29=7%2Fsqrt%28170%29=%287%2F170%29sqrt%28170%29
beta=33%2F%283sqrt%28170%29%29=11%2Fsqrt%28170%29=%2811%2F170%29sqrt%28170%29
delta=0%2F%283sqrt%28170%29%29=0