# Vector's projection online calculator

*Projection of the vector*
to the axis l is called the scalar, which equals to the length of the segment
A_{l}B_{l},
and point A_{l} is the projection of point
A to the direction of the l axis, point
B_{l} is the projection of the point
B to the direction of the l-axis:

From the elementary geometrical considerations, follows:

pr_{l} =
A_{l}B_{l} =
AB ∙ cos α =
| | ∙ cos α

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

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

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

, where φ - angle between vectors и .

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.