How do you find the unit vector that has the same direction as the vector from the point A= (5, 2) to the point B= (3, 2)?

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Answer 1 · 2017-01-07T09:10:10

$((-1),(0))=-hatveci$

if $A$ has coordinate $(5,2)$ then its position vector is given by

$vec(OA)=5hatveci+2hatvecj=((5),(2))$

if $B$ has coordinate $(3,2)$ then its position vector is given by

$vec(OB)=3hatveci+2hatvecj=((3),(2))$

The vector from $A$ to $B$ is:

$vec(AB)=vec(AO)+vec(OB)$

$vec(AB)=-vec(OA)+vec(OB)$

$vec(AB)=-((5),(2))+((3),(2))$

$vec(AB)=((-5+3),(-2+2))=((-2),(0))$

call this vector $vecd$

A unit vector in this direction is given by

$hatvecd=(vec(d))/|vecd|$

$vecd=((-2),(0))=>|vecd|=2$

$hatvecd=1/2((-2),(0))=((-1),(0))$