How do you find the unit vector of v=4i+2j?

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Answer 1 · 2016-11-28T18:01:38

The answer is #=2/sqrt5i+1/sqrt5j#

The unit vector of #vecv# is

#hatv=vecv/(∥vecv∥)#

#vecv=4i+2j=〈4,2〉#

#∥vecv∥=sqrt(16+2)=sqrt20=2sqrt5#

Therefore,

#hatv=1/(2sqrt5)〈4,2〉=〈2/sqrt5,1/sqrt5〉#

Answer 2 · 2016-11-28T18:02:59

#(4/sqrt20, 2/sqrt20)#

#vecv# is (4,2) Its magnitude #||vec v|| =sqrt(4^2 +2^2)= sqrt20#

Hence unit vector would be #(4/sqrt20, 2/sqrt20)#