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)?

Question

11562 views around the world

You can reuse this answer
Creative Commons License

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))#