How do you find a unit vector in the direction of the vector v=(-3,-4)?

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Answer 1 · 2016-08-06T17:10:52

#(-3/5,-4/5)#.

The reqd. vector is in the direction of #vecv=(-3,-4)#.

Therefore, it must be of the form

#k(-3,-4)=(-3k,-4k), where, k>0#

As this is a unit vector, #||((-3k,-4k))||=1#.

#:. sqrt{(-3k)^2+(-4k)^2}=1#.

#:. 5k=1 rArr k=+-1/5, but, k>0 rArr k!=-1/5. :. k=1/5#.

Hence, the unit vector#=(-3/5,-4/5)#.