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# Unit Vector Calculator

Select the no of variables, Insert the values, and press calculate button using unit vector calculator

Table of Contents:

## Unit Vector Calculator

Unit vector calculator is used to calculate the unit vector of a given vector. This calculator takes the coordinates values of 2 and 3-dimensional vectors performs the necessary calculations to determine the unit vector and displays the result.

## What is a Unit Vector?

A vector with a magnitude of 1 unit is referred to as a unit vector. It is also known as a directed vector. It is indicated by a lowercase letter that also has the capitalization symbol ('') next to it. By dividing it by vector magnitude as shown below, any vector may easily be transformed into a unit vector.

General formula

**Vˆ= V / ∣V∣**

## How to calculate unit vectors?

**Example 1**

Find the unit vector of v = 2i+3j

**Solution**

**Step** **1**:The magnitude of the vector

V = √(x^{2}+y^{2})

∣V∣= √(2^{2}+3^{2})

∣V∣= √(4+9)

∣V∣= √ 13

**Step 2: **Take the formula and place the values of the vector and magnitude.

Vˆ= (V_{1}, V_{2}) / ∣V∣

Vˆ= V_{1}/∣V∣, V_{2} / ∣V∣

Vˆ= (2/√13,3/√13)

**Example 2**

Find the unit vector of v = 2i +2j+3k

**Solution**

The given input vector V= (2,3,2)

General formula Vˆ= V / ∣V|

**Step** **1**: Take the magnitude of the vector

V = √ (x^{2}+y^{2}+z^{2})

∣V∣=√ (2^{2}+2^{2}+3^{2})

∣V∣=√4+4+9

∣V∣=√17

**Step** **2**: Put the values into the general formula

Vˆ= (V_{1}, V_{2}, V_{3}) / ∣V∣

**Vˆ= V _{1}/∣V∣, V_{2} / ∣V∣, V_{3}/∣V∣**

Vˆ= (2/√17,2/√17,3/√17)