SOLUTION: What unit vector is in the same direction as v = 2i - 4j? Show all work.

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Question 1202476: What unit vector is in the same direction as v = 2i - 4j?
Show all work.

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

The unit vector is the given vector divided by the modulus, which is another name
for the length of the vector.


The length of the given vector is  L = sqrt%282%5E2+%2B+%28-4%29%5E2%29 = sqrt%284+%2B+16%29 = sqrt%2820%29 = 2%2Asqrt%285%29.


Therefore, the unit vector in this problem is

    v%5Bunit%5D = %281%2Fsqrt%285%29%29*i - %282%2Fsqrt%285%29%29*j,


which is the same as

    v%5Bunit%5D = sqrt%285%29%2F5*i - %282%2Asqrt%285%29%29%2F5*j.

Solved.