This free online calculator help you to find a projection of one vector on another.

Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to find a projection of one vector on another.

Calculator

Guide

Some theory

Vector projection calculator

Dimension of a vectors:
Form of first vector representation:
Form of second vector representation:

Input vectors:

First vector

= {,

,

}

Second vector

= {,

,

}

Guide - Vector projection calculator

To find projection of one vector on another:

Select the vectors dimension and the vectors form of representation;

Type the coordinates of the vectors;

Press the button "Find vector projection" and you will have a detailed step-by-step solution.

Entering data into the vector projection calculator

You can input only integer numbers or fractions in this online calculator. More in-depth information read at these rules.

Additional features of the vector projection calculator

You can navigate between the input fields by pressing the keys "left" and "right" on the keyboard.

Theory. Projection of one vector on another

Definition. Projection of the vector AB on the axis l is a number equal to the value of the segment A_{1}B_{1} on axis l, where points A_{1} and B_{1} are projections of points A and B on the axis l.

Definition. The vector projection of a vector a on a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b.

Vector projection - formula

The vector projection of a on b is the unit vector of b by the scalar projection of a on b:

proj_{b}a =

a · b

b

|b|^{2}

The scalar projection of a on b is the magnitude of the vector projection of a on b.