Vector u
Vector v
Projection of a onto b

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.

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 ba = a . b/|b|2b 	

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).


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

Proj ba = a . b/|b|2b 	 

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.

Projba = 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 ba = 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.