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

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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) About Me  (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

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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 %284%2Fsqrt%2833%29%29i+-+%281%2Fsqrt%2833%29%29j+-+%284%2Fsqrt%2833%29%29k