Vector's projection online calculator

Projection of the vector vector a to the axis l is called the scalar, which equals to the length of the segment AlBl, and point Al is the projection of point A to the direction of the l axis, point Bl is the projection of the point B to the direction of the l-axis:

vector's projection to the axis definition

From the elementary geometrical considerations, follows:

prl vector a = AlBl = ABcos α = | vector a | ∙ cos α

It's very easy to calculate the projection of the arbitrary vector vector a to any decart axis, for instance, x-axis. Here we have, cos α is the directional cosine of the vector vector a:

projection on x-axis formula

Therefore, projection of the arbitrary vector vector a on the decart axis equals to corresponding coordinate of the vector.

A little bit complicated to calculate the projection of the abritrary vector vector a to the arbitrary axis or arbitraty vector vector b. In this case, we need to calculate the angle between corresponging vectors, what can be done by using the vectors scalar product formula:

projection of the vector to another vector formula

, where φ - angle between vectors vector a и vector b.

Our online calculator is able to find the projection of one arbitrary vector to the another arbitraty vector with step by step solution for free.

Input vectors dimension

Vectors dimension
Vector vector A representations form:
Vector vector B representation form:
Vector vector A = { }
Vector vector A:
Vector vector B = { }
Vector vector B: