# Vector Projection Calculator

Finding the projection of **one** vector on the other is a technical **task**. It is because you have to find the **connection** between two **vectors **that are neither **parallel** nor perpendicular. You might be unable to understand how it all goes **unless** you have used the “**Vector Projection Calculator**”. This online calculator can **help** you in finding the projection of **one** vector to the other without being proficient in it.

You can **use** this **maths calculator** easily without using a complex method. It has a **simple** interface that can be understood by **students** of all grades. Just input the values in this maths calculator to get the projection of one vector to the **other** quickly.

**Table of Contents**

## What is vector projection?

The **vector** projection is the **orthogonal** projection of **one** vector to the other **horizontal** vector. In simple **words**, if we **connect** a horizontal vector with an orthogonal vector, the **perpendicular **drawn from the orthogonal vector to the **horizontal** vector will be the vector **projection**. This particular **term** is used in different Mathematical and **Physics-related** problems.

Using the vector projection **approach**, one can **easily** find the area **bounded** by a specific **motion** of a vehicle. **Also**, it is useful in finding the **angle** of projection for a plane or **missile**. Multiple practical problems are **based** on this approach that professionals **use** in their fields.

### What is the vector projection formula?

To find the projection of one vector to the **other**, you can use the simple **formula** mentioned below. **Suppose** we have two vectors “**a**” and “**b**”, the projection of vector “**a**” to “**b**” will be given as

Proj b^{a}= a . b/|b|^{2}b

### How to calculate the vector projection?

If you are **proficient** in the dot **product**, this calculation will be pretty **simple** for you. But we have also solved an **example** here to let you understand the process **properly** and find vector projection without **mistakes**.

**Example 1:**

Find the projection on Vector A (2, 5, 7) by Vector B (3, 9, 5).

**Solution:**

As we know that the formula for finding the projection of B on A is,

Proj b^{a}= a . b/|b|^{2}b^{ }

So, we have to find the values to **put** them in the above **formula**. Let’s **start** with the dot product of vectors A and B.

A . B = (2 x 3) + (5 x 9) + (7 x 5)

= 6 + 45 +35

= 86

Now, we have to find the mod of **vector** B as we need it in the **denominator** of the above formula. So,

|B| = √(3)^{2}+ (9)^{2}+ (5)^{2}

= √9 + 81 + 25

= √115

As we have all the required **values**, so let’s put them in the formula given **above** for the calculation of the projection of **B** on **A**.

Projb^{a}= 86/|115|^{2}(3, 9, 5)

= 86/115 (3, 9, 5)

= (258/115 , 774/115 , 130/115)

### How to use the vector projection calculator?

As you can say it will take **time** to find the **projection** of a vector on the other. Also, it is **possible** that you make mistakes when you have **complex** components for a **vector**. To make the process easier, you should use this online tool by Calculator’s Bag. Here are the **steps** that you have to adopt for using this online calculator.

- Write the components of the first vector
- Write the components of the second vector
- This calculator will automatically find the vector projection in terms of all three components and display it on the screen

### FAQ | Vector Projection Calculator calculator

**What are the applications of a vector projection calculator?**

Using this calculator, you can find the projection of one vector to the other. It is used in multiple professional tasks like the angle for trajectory motion, area coverage, and others.

**Can the vector projection calculator handle vectors in multiple dimensions? **

Yes, this vector projection calculator can handle vectors having components in all three dimensions.

**Can two vectors have the same projection?**

Yes, if two vectors are exactly equal to each other, their projection can be the same.

**Is vector projection a scalar? **

No, vector projection is also a vector as it involves the vector on which the projection is made.

**How to calculate vector projection? **

To calculate the vector projection, you have to use the following formula

Proj b^{a}= a . b/|b|^{2b}^{ }

**What is the projection of a vector onto itself? **

The projection of a vector on itself will be the magnitude of that vector.