Final answer:
To verify that eigenvectors are mutually orthogonal, the dot product between them should equal zero, indicative of a 90° angle and hence their perpendicularity.
Step-by-step explanation:
To check whether a pair of eigenvectors are mutually orthogonal, you must determine if their scalar, or dot, product equals zero. If two eigenvectors ℝ and ℞ are mutually orthogonal, the calculation ℝ ⋅ ℞ will result in zero, signifying that they are perpendicular to each other in space. This is because the scalar product between two orthogonal vectors is zero as it involves multiplying their magnitudes with the cosine of the angle between them, which is 90° for orthogonal vectors, resulting in a product of zero. Moreover, vector components in a polar coordinate system facilitate the inspection of orthogonality, as orthogonal vectors would have components that reflect their perpendicular nature in the system.