Given:
#color(red)(vec v = -3i = <-3,0>)#
The Formula to find the Unit Vector #vec u# is
#color(green)(vec u = (vec v)/|| vec v||#, where
#|| vec v||# is the Magnitude of Vector #vec v#
#vec u = 1/||vec v||*vec v#
#vec u = 1/(sqrt((-3)^2 + (0)^2))*<-3,0>#
#vec u = 1/sqrt(9)*<-3, 0>#
#vec u = 1/3*<-3, 0># This is Scalar Multiplication
We have multiplied the Scalar Value #1/3# by each of the components of Vector #vec v#
Hence, we get
#<-3/3, 0/3>#
#color(blue)(rArr <-1, 0>)#
We can also write this as #color(blue)(vec u =-i)#
#color(blue)(vec u =-i)# is our Unit Vector in the direction of the given vector #vec v = -3i#
We can also verify this solution by finding the Magnitude of the vector #color(blue)(vec u =<-1,0>#
The Magnitude of the vector must be equal to one
Let us now find
#||<-1, 0>||#
#rArr sqrt((-1)^2 + (0)^2)#
#rArr sqrt((1) + (0))#
#rArr sqrt(1)#
#rArr 1#
Hence, verified.
Hope you find this solution useful.
