SOLUTION: What is the unit vector directed oppositely to the vector <-4i + j + 4k>?
(My approach was to find the unit vector first, then reverse the signs. is this correct?)
Thank you
Algebra.Com
Question 976985: What is the unit vector directed oppositely to the vector <-4i + j + 4k>?
(My approach was to find the unit vector first, then reverse the signs. is this correct?)
Thank you for your time and help!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Your approach is correct. You can also reverse the signs, then find the unit vector. It doesn't matter either way.
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Magnitude of vector
v = -4i + j + 4k
|v| = sqrt(a^2 + b^2 + c^2)
|v| = sqrt((-4)^2 + (1)^2 + (4)^2)
|v| = sqrt(33)
|v| = 5.74456264653802
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Divide each component by the magnitude
-4/5.74456264653802 = -0.6963106238228
1/5.74456264653802 = 0.1740776559557
4/5.74456264653802 = 0.6963106238228
-------------------------------------------------------
The unit vector is -0.6963106238228i + 0.1740776559557j + 0.6963106238228k
Flip the signs: 0.6963106238228i - 0.1740776559557j - 0.6963106238228k
This final answer is approximate. If you want the exact answer in terms of radicals, use sqrt(33) in place of 5.74456264653802
So the exact answer would be
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