Introduction to Unit Vector Calculator:
Unit vector calculator is the best online source that helps you to find the unit vector of a given vector function. It is used to compute the vector function for normalization by dividing each term by its corresponding magnitude value.
The unit vector notation calculator is an educational tool that helps teachers, students, and parents teach their children about the concept of unit vector concept without sending them to any tutor by using its stepwise calculation method for finding the unit vector solution.
What is Unit Vector?
Unit Vector is a type of vector that has a magnitude of 1 as it indicates direction without specifying the magnitude of the original vector function. It simplifies the process of finding normalizing vectors of a vector function.
This method is used to find the direction of a vector without considering its magnitude because in a vector magnitude and direction are important components. It is used in fields like physics, engineering, and graphic design.
Formula of Unit Vector:
The formula of unit vectors is used to normalize the vector function whose have a magnitude is 1 only for 2-D or 3-D space.
$$ u \;=\; \left( \frac{x}{||v||},\; \frac{y}{||v||} \right) $$
$$ u \;=\; \left( \frac{x}{||v||},\; \frac{y}{||v||},\; \frac{z}{||v||} \right) $$
Whereas,
||v|| = is the magnitude of function f(x,y,z)
u = unit vector direction of a function
How to Calculate The Unit Vector?
To calculate the unit vector you need to know the vector quantities and its types so that you cannot confuse the direction and magnitude of a vector function. Here is the calculation process of calculating the unit vector function in steps.
Step 1:
Determine the unit vector function F(x,y) or F(x,y,z) in two-dimensional or three-dimension space respectively.
Step 2:
Find the magnitude of a given vector function using this formula for 3-D which is given as:
$$ ||v|| \;=\; \sqrt{x^2 + y^2 +z^2} $$
You can also modify the magnitude formula for two-dimension space.
Step 3:
After calculating the magnitude, use the below formula for the unit vector of a given function, in which divide each term by its magnitude to get a solution.
$$ u \;=\; \left( \frac{x}{||v||},\; \frac{y}{||v||},\; \frac{z}{||v||} \right) $$
Step 4:
Simplify it, if needed to simplify the unit vector of a given vector function.
Solved Example of Unit Vector:
The solved example of a unit vector function gives you a better understanding about the conversion of unit vectors.
Example: Find the unit vector in the direction of the vector
$$ v \;=\; (3, -4,12) $$
Solution:
The given vector function is,
$$ v \;=\; (3, -4, 12) $$
First, find the magnitude of a given vector using the below formula,
$$ ||v|| \;=\; \sqrt{x^2 + y^2 + z^2} $$
Add the value of above vector function as x = 3, y = -4, z = 12 to get magnitude value,
$$ || v || \;=\; \sqrt{3^2 + (-4)^2 + 12^2} $$
Simplify it,
$$ 9 + 16 + 144 \;=\; 169 $$
$$ ||v|| \;=\; \sqrt{169} \;=\; 13 $$
For unit vector divide each term of a function to its magnitude such as,
$$ u \;=\; \left( \frac{x}{||v||},\; \frac{y}{||v||},\; \frac{z}{||v||} \right) $$
Add the value to get the solution of the unit vector function in three dimensions,
$$ u \;=\; \left( \frac{3}{13},\; \frac{-4}{13},\; \frac{12}{13} \right) $$
How to Use the Normal Unit Vector Calculator?
Unit vector notation calculator has a user-friendly design that enables you to find the unit vector of given vector questions easily. Before adding the input function value problems, you just need to follow our instructions. These instructions are:
- Enter the unit vector function in two or three dimensions in the input box to find the unit vector questions.
- Recheck your input vector function value before hitting the calculate button to start the calculation process in the unit vector addition calculator.
- Click on the “Calculate” button to get the desired result of your given unit vector problems.
- If you want to try out our unit vector angle calculator for the first time, you can use the load example to learn and see how efficiently our tool works.
- Click on the “Recalculate” button to get a new page for solving more unit vector problems and their solutions.
Output of Unit Vector Between Two Points Calculator:
Unit vector notation calculator gives you the solution to a given problem when you add the input to it. It provides you with solutions that may include the following:
- Result Option:
You can click on the result option, and it provides you with a solution to the unit vector problem of your given function.
- Possible Step:
When you click on the possible steps option, it provides the solution to unit vector problems in steps.
Useful Features Of Unit Vector Calculator 3D:
Unit vector formula calculator provides you with many useful features that help you to calculate unit vector problems and give you a solution without any trouble. These features are:
- Unit vector direction calculator is a free-of-cost tool so you can use it for free to find unit vector problem solutions without paying anything.
- The unit vector notation calculator is an adaptable tool that can manage various types of vector functions to calculate the unit vector function solution.
- Our unit vector addition calculator helps you to get conceptual clarity for the unit vector process when you use it for practice and when you use it to solve more examples.
- It saves the time that you consume on the calculation of the unit vector of the given vector function problems.
- Unit vector in direction calculator is a reliable tool that provides you with accurate solutions whenever you use it to determine the unit vectors without any errors in calculation.
- Unit vector between two points calculator provides the solution without imposing any restriction which means you can use it multiple times unlimitedly.
- It ensures efficiency and accuracy in solving unit vector tasks using the unit vector formula process.
