Question

How do you find the unit vector in the direction of the given vector u=<-2,2>?

Answer 1

`=-i/(sqrt2)+j/(sqrt2) or<-1/(sqrt2),1/(sqrt2)>`

Explanation:

`|u| =sqrt((-2)^2+2^2)`
`|u| =sqrt(4+4)`
`|u| =sqrt(8)`
`|u| =sqrt(4*2)`
`|u| =2sqrt(2)`

Unit Vector `=1/|u|(-2i+2j)`
`=1/(2sqrt2)(-2i+2j)`

`=1/(cancel2sqrt2)*cancel2(-i+j)`

`=1/(sqrt2)(-i+j)`

`=-i/(sqrt2)+j/(sqrt2)`