Final answer:
The orthogonal complement, orthba, is a vector representing the part of vector a perpendicular to vector b, calculated by subtracting the projection of a onto b from a.
Step-by-step explanation:
The orthogonal complement of a vector a with respect to another vector b is given by the expression orthba = a - projba. This is a mathematical concept found in the field of linear algebra and vector analysis. The orthogonal complement essentially represents the vector component of a that is perpendicular to b.
To compute the orthogonal complement, one first calculates the projection of a onto b, which is given by the formula projba = (a · b / b · b) * b. This projection is a vector that lies in the direction of b and represents the component of a that is parallel to b. Subsequently, by subtracting this projection from the original vector a, we obtain orthba, the component of a that is orthogonal to b.
Understanding the orthogonal complement is fundamental in studying concepts such as orthogonality, vector spaces, and their applications in various fields including physics and engineering.