# Finding values to make a unit vector

## 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.

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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
Mentor

## 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.