Question

Let u= <4,3>. Find the unit vector in the direction of u, and write your answer in component form.

Answer 1

Take the vector u = <ux, uy> = <4, 3>.

Find the magnitude of u:

||u|| = sqrt[ (ux)^2 + (uy)^2]

||u|| = sqrt[ 4^2 + 3^2 ]

||u|| = sqrt[ 16 + 9 ]

||u|| = sqrt[ 25 ]

||u|| = 5

To find the unit vector in the direction of u, and also with the same sign, just divide each coordinate of u by ||u||. So the vector you are looking for is

u/||u||

u * (1/||u||)

= <4, 3> * (1/5)

= <4/5, 3/5>

and there it is.

Writing it in component form:

= (4/5) * i + (3/5) * j

I hope this helps. =)