Find the unit vector

Question

Find the unit vector that's in the same direction as w=20i-21j

Answer 1

Given vector w has a certain length (L).  Calculate that!

 

Then u = <20/L, -21/L>

Answer 2

If u = ai + bj is a vector in two dimensional space, then                 llull = √(a²+b²) is the magnitude (length) of u.  The vector (1/llull)u is a unit vector (a vector of length 1) that is in the same direction as u.

 

So, for w = 20i-21j, llwll = √[(20)²+(-21)²] = 29

 

A unit vector in the same direction as w is                                            

                      (1/llwll)w = (20/29)i - (21/29)j