Unit Vector Calculator

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

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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


Step 1:The magnitude of the vector 

V = √(x2+y2)

∣V∣= √(22+32)

∣V∣= √(4+9)

∣V∣= √ 13

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

Vˆ= (V1, V2) / ∣V∣

Vˆ= V1/∣V∣, V2 / ∣V∣

Vˆ= (2/√13,3/√13)

Example 2

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


The given input vector V= (2,3,2)

General formula Vˆ= V / ∣V|

Step 1: Take the magnitude of the vector

V = √ (x2+y2+z2)

∣V∣=√ (22+22+32­­)



Step 2: Put the values into the general formula

Vˆ= (V1, V2, V3) / ∣V∣

Vˆ= V1/∣V∣, V2 / ∣V∣, V3/∣V∣

Vˆ= (2/√17,2/√17,3/√17)

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