Question #2ad9d

1 Answer
Jan 10, 2018

The Unit Vector #color(blue)(vec u = -i)# is in the direction of the given vector #color(red)(vec v = -3i)#

Explanation:

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.