What does it mean for vectors to be orthogonal?

Vectors being orthogonal means that they are perpendicular to each other in a geometric sense. This property is mathematically defined by the dot product of the two vectors. Specifically, two vectors are considered orthogonal if the result of their dot product equals zero. This condition arises because the dot product can be expressed in terms of the magnitudes of the vectors and the cosine of the angle between them. If two vectors are orthogonal, the angle between them is (90^\circ), and the cosine of (90^\circ) is zero, which results in a dot product of zero.

Therefore, the correct definition correlates directly with the concept of orthogonality in linear algebra. Understanding this definition is crucial, especially when dealing with concepts such as vector spaces, projections, and least squares, where orthogonality plays a significant role in simplifying computations.