Unit Vector Calculator

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 = √(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

Solution

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+3^2­­)

∣V∣=√4+4+9

∣V∣=√17

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)