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 AlBl, and the 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, it follows:

прl = AlBl = ABcos α = | | ∙ cos α

It's very easy to calculate the projection of the arbitrary vector to any decart axis, for instance, -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 and .

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.

Vector projection calculator
Vector A by:
Vector B by:
Vector A = { }
Vector B = { }

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