How do you find the unit vector in the direction of the given vector of $v=i+j$ ?

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Answer 1 · 2017-01-11T13:54:27

$hatvecv=sqrt2/2(hatveci+hatvecj)$

By definition a unit vector has a magnitude (modulus) of 1. So to find a unit vector of any given vector in that direction we work out:

$hatvecv=vecv/|vecv|$

in this case

$vecv=hatveci+hatvecj$

$|vecv|=sqrt(1^2+1^2)=sqrt2$

$hatvecv=1/sqrt2(hatveci+hatvecj)$

$hatvecv=sqrt2/2(hatveci+hatvecj)$

How do you find the unit vector in the direction of the given vector of v=i+jv=i+j?