# Finding values to make a unit vector

1. Sep 17, 2012

### Sammy600

1. The problem statement, all variables and given/known data
Find all values of a such that w=ai+$\frac{a}{8}$j is a unit vector.

2. Relevant equations
unit vector has length of 1. and for a vector v unit vectors would be v/magv

3. The attempt at a solution
1=magw=\sqrt (a2+(a/8)2)
1=a2+(a2/64)
64=2a2
32=a2
a=$\sqrt{32}$

i know that the solution is: +/- $\frac{8}{\sqrt{65}}$ but am at a loss as to how it was obtained. any help is appreciated.

2. Sep 17, 2012

### damabo

sqrt(a^2+a^2/64)=1
so this means sqrt((64a^2+a^2)/64)=1
so sqrt(65a^2/64)=1
this means 65a^2/64=1
and then you get the result

3. Sep 17, 2012

### Staff: Mentor

Your mistake is above. Multiply each term on the right side by 64. You don't get 2a2.