*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 the 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, it follows:

пр_{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, -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

by:

by:

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