# Unit Vector Calculator

One of the most **studied** branches of Mathematics is **Vector** Mathematics in which you have to **deal** with vectors. In this **field**, you don’t only deal with **numbers** but also with **directions** of the given measurements. Some calculations are **common **in this field and **need** to be understood by **everyone**.

Unit **vector** calculation is **one** that has **great** importance in the real life as well as with **educational** aspects. It is **neither** difficult to do so nor easy because you should be aware of **vector** mathematics. With the help of this **unit vector calculation**, you can easily make this **process** easier. This maths calculator can find a unit vector **easily** using your inserted **values** for a particular vector.

**Table of Contents**

## What is a unit vector?

It is a specific vector that has a **magnitude** equal to **1** with a specific **direction**. A unit vector is **normally** used to **show** the direction of **any** measurement or vector. The **length** of this particular vector **must** be 1 because of which it is given the **name** of the unit vector.

It is used **widely** in Physics and **Mathematics **to represent the direction of **any** measurement like **Force**, Distance, etc. A unit vector is **represented** by writing a cap (**^**) on the **name** of the vector that will be an **alphabet**.

### Unit vector formula

To **find** a unit vector for any **specific vector**, we need to **use** a particular formula. Here is the general **formula** you should use for **finding** the unit vector for **any** particular vector.

a = a/|a|

Here, the unit vector is on the **left** side of the **equation** while the **numerator** on the right **side** is the vector and the denominator is the **magnitude** of the vector that is **calculated** by using the coordinates of **x**, **y**, and z axes.

### How to calculate unit vectors with ease?

No **doubt**, you have learned the **formula** used to find the **unit** vector. But you may not **know** how to find this vector **step** by **step**. So, we have **shared** the steps here by following which you can **easily** find the unit vector of **any** given vector.

- Find the magnitude of the vector by addition of the squares of the coordinates and then taking the square root of the final answer
- Divide the magnitude by every coordinate of the given vector
- In the end, you will get the coordinates of the unit vector.

For your better understanding, we have solved an example here. Go through it to learn how this process is completed.

**Example 1:**

If the vector u has coordinates (5, 6, 9), then what will be the coordinates of the unit vector?

**Solution:**

As mentioned earlier, we have to find the magnitude of “u”. For this, we need to use the following formula, So,

|u| = √x^{2}+ y^{2}+ z^{2}

From the given data, we know that:

x = 5

y = 6

z = 9

So,

|u| = √5^{2}+ 6^{2}+ 9^{2}

= √25 + 36 + 81

|u| = 11.92

Now, we have to use the above formula and divide all coordinates with this magnitude. So, the coordinates for the unit vector will be,

x = 5/11.92

= 0.42

y = 6/11.92

= 0.5

z = 9/11.92

= 0.76

It means the unit vector for the given vector “u” will be (0.42, 0.5, 0.76).

### How to use the unit vector calculator?

As you can see it will be a **hectic** process to find the unit vector through a manual **approach**. To make the process simpler and **faster**, you can use this online tool Calculator’s Bag. Just follow these steps to use this tool.

- Write the “x”, “y”, and “z” coordinates of the given vector
- This calculator will automatically show you its magnitude and the coordinates for the unit vector

### FAQ | Unit Vector Calculator

**What two unit vectors make an angle of 60 with v 8i 6j?**

The two vectors that make an angle of 60 with v having coordinates (8, 6) will be (2/5 +√5/10, 3/10 + 2√5/15 ) and (2/5 -√5/10, 3/10 - 2√5/15).

**Is (1, 1) a unit vector? **

No, (1, 1) is not a unit vector.

**Are all unit vectors equal?**

No, because unit vectors may have different directions.

**Can the unit vector calculator handle negative vectors? **

Yes, this calculator can handle either positive or negative vectors.

**What is the difference between a position vector and a unit vector? **

A position vector shows the position of any point or object and can have any magnitude. But a unit vector can have only 1 magnitude with any direction.