Finding values to make a unit vector

[Sammy600]

Homework Statement

Find all values of a such that w=ai+$\frac{a}{8}$j is a unit vector.

Homework Equations

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

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.

 

[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

 

[Mark44]

Homework Statement

Find all values of a such that w=ai+$\frac{a}{8}$j is a unit vector.

Homework Equations

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

The Attempt at a Solution

1=magw=\sqrt (a²+(a/8)²)
1=a²+(a²/64)
64=2a²

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