If you have two vectors, it can be useful to think of the first one as the sum of two vectors:

one vector in the same direction as the second vector, and

one vector perpendicular to the second vector.

Here A is the first vector and B is the second. The light blue vector is in the same direction as B, and is called the Projection of A on B. The red vector is perpendicular to B; it can be called the Orthogonal Projection. To confuse things, often the projection itself is called the Orthogonal Projection.


CalGraph calculates both.


Enter the two vectors.


Click to find the Projection of A onto B and to find the orthogonal projection.


You can find the Projection of B onto A, and its orthogonal projection using and .


Projection of vectors only works if both vectors have the same dimension.