Vector's projection online calculator

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Projection of the vector vector a 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 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:

прxaacosαax

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:

прbaacosφaabababb

, where φ - angle between vectors vector a and 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.

Vector projection calculator
Vector A by:
Vector B by:
прbaпр54312
Vector A = { }
Vector B = { }


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