## Introduction to Vector Direction Calculator:

Vector direction calculator is an online tool that helps you to **find the direction** of a given vector function or points. It is used to compute the orientation of a vector in multidimensional space in a fraction of seconds.

Direction vector calculatoris a beneficial tool for students, teachers or researchers as it simplifies the process of finding direction of a vector calculation and provides accurate results which make it easy for you to interpret the vector's orientation/direction.

## What is Direction of the Vector?

Direction of the vector is used to find the angle of the given vector along the x-axis in a horizontal direction.The vector has a pointed arrow toward the direction and magnitude at a fixed point in that direction on a graph.

A directional vector is denoted with the symbol** a** = â.|a| in which **a **is indicate the direction and â is the unit vector, |a| is the magnitude of a vector a.

## Formula of Direction of the Vector:

The formula of direction of a vector depends on the angle at your vector function is moving in two or three dimensional space.

**For 2 - D**:

$$ \theta arctan \left(\frac{v_y}{v_x} \right) $$

**For 3 - D**:

$$ \varnothing \;=\; arctan \left( \frac{v_y}{v_x} \right) $$

## How to Calculate the Direction of the Vector?

To calculate the direction of the vector in two or three dimensions, the vector direction calculator finds the angle of that vector function. Lets see how to calculate the angle of a vector that points out the direction along which a vector is moving at a specific point in steps.

**Step 1**:

Identify the vector function and the point value of x and y.

**Step 2**:

Use the formula of direction of the vector whether it is in 2-D or 3-D space as per your needed.

$$ \theta \;=\; arctan \left( \frac{v_y}{v_x} \right) $$

**Step 3**:

Add the x and y value and find the arctan value for the angle of the given vector function.

**Step 4**:

After finding the angle draw a graph as per the calculation of a given vector function.

## Solved Example of Direction of the Vector:

The solved example of direction of the vector helps you to understand how the direction of vector calculator solves such problems.

### Example: To approximate the direction of the vector,

$$ \vec{v} \;=\; \langle 5, -8 \rangle $$

**Solution**:

The given vector is in 2-D,

$$ \vec{v} \;=\; \langle 5, -8 \rangle $$

$$ x \;=\; 5 \;and\; y \;=\; -8 $$

Use the direction of a vector formula which is,

$$ \theta \;=\; tan^{-1} \frac{y}{x} $$

Put x and y value in it,

$$ \theta \;=\; tan^{-1} \frac{-8}{5} $$

The solution of the direction of the vector is,

$$ \theta \;=\; -57.99^{\circ} $$

The exact angle of the direction of vector along x-axis,

$$ \theta \;=\; 360^{\circ} - 57.99^{\circ} \;=\; 302.005^{\circ} $$

$$ \theta \;=\; 302^{\circ} $$

The graph of a direction of a vector function is:

## How to Solve the Direction of Vector Calculator?

Vector direction calculatorhas a simple design that makes it easy for you to understand how to evaluate the angle of the given vectors only by following our instructions that are given as:

- Enter the value of the direction vector function to find the angle in the input box.
- Review the given vector before hitting the calculate button to start the evaluation process in the direction vector calculator.
- Click the “Calculate” button to get the result of your given vector problem in direction angle of a vector calculator.
- If you are trying our directional vector calculator for the first time then you can use the load example to learn more about this method.
- Click on the "Recalculate" button to get a new page for finding more example solutions of direction vector problems.

## Final Result Of Direction Of A Vector Calculator:

Direction of the vector Calculator gives you the solution from a given vector when you add the input into it. It provides you with solutions that is:

**Result Option**:

When you click on the result option the direction of vector calculator gives you a solution to the angle of the direction vector problem.

**Possible Steps**:

When you click on it, this option will provide you with a solution where all the calculations of Direction of the vector process steps are mentioned.

**Plot Option**:

The plot option give you solution of direction of the vector problem.

## Benefits Of Vector Direction Calculator:

Direction angle of a vector calculator provides you with many benefits that help you to calculate direction of vector problems and give you a solution without any trouble. These benefits are:

- Direction of a vector calculator is a free-of-cost tool so you can use it for free to find directions for vector problem solutions without paying.
- It is an adaptable tool that can manage various types of vectors to calculate the direction of a vector in which it moves.
- Our directional vector calculator helps you to get conceptual clarity for the direction vector process when you use it for practice by solving more examples.
- The direction vector calculator saves the time that you consume on the calculation of the direction of vector problems along the x-axis.
- The direction of vector calculatoris a reliable tool that provides you with accurate solutions whenever you use it to calculate the direction of a vector without any errors in calculation.
- Direction of the vector calculatorprovides the solution without imposing any restriction which means you can use it multiple times.
- Direction angle of a vector calculator ensures efficiency and accuracy in solving the direction of the vector using the direction vector process.