# Finding values to make a unit vector

• Sammy600
In summary, the conversation is about finding all values of a such that the vector w=ai+\frac{a}{8}j is a unit vector. The solution is +/- \frac{8}{\sqrt{65}}, which was obtained by setting the magnitude of w equal to 1 and solving for a. However, there was an error in the attempt at a solution, as the equation 1=magw=\sqrt (a2+(a/8)2) was incorrectly simplified to 64=2a2 instead of 64=a2.
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.

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

Sammy600 said:

## 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.
Sammy600 said:
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.

## 1. What is a unit vector?

A unit vector is a vector with a magnitude of 1 and is typically denoted by a hat (^) symbol above the vector's variable. It is used to represent direction without any consideration for length or scale.

## 2. Why is it important to find values to make a unit vector?

A unit vector is important because it helps to simplify and standardize calculations in vector operations. It also represents a direction without being affected by the length or scale of the vector, making it useful in various applications such as physics, engineering, and computer graphics.

## 3. How do you find values to make a unit vector?

To find values to make a unit vector, you first need to calculate the magnitude of the vector. Then, divide each component of the vector by its magnitude. This will result in a vector with a magnitude of 1, making it a unit vector.

## 4. Can any vector be turned into a unit vector?

Yes, any vector can be turned into a unit vector by following the steps mentioned above. It is important to note that the vector must have a non-zero magnitude in order for it to be converted into a unit vector.

## 5. What is the significance of unit vectors in physics?

In physics, unit vectors are used to represent direction in a three-dimensional coordinate system. They are essential for solving problems involving force, velocity, acceleration, and other vector quantities. Additionally, unit vectors allow for simplification of calculations and provide a standard way of representing direction in different physical systems.

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