Final answer:
Two continuous-time functions u(t) and v(t) are orthogonal on the interval (a, b) if their product integrated over that interval equals zero, suggesting no overlap in signal space. This concept connects to the broader topics of vectors and function properties in mathematics and physics.
Step-by-step explanation:
Two continuous-time functions u(t) and v(t) are said to be orthogonal on the interval (a, b) if the integral of their product over that interval is zero. This implies that these functions do not have any overlap in the signal space when integrated over the specified interval.
As per the provided contexts, which seem to include topics from physics and calculus, orthogonality is often discussed in the setting of vectors and functions. For instance, in mechanics, the acceleration vector is constant (a(t) = ai + bj + ck m/s²), suggesting that if the acceleration components (a, b, and c) are not zero, then the velocity function V(t) is a linear function of time due to the direct integration of acceleration.
Overall, while the context provided ranges from the definition of orthogonal functions to vector calculus in physics, it is critical to understand that orthogonal functions have distinct properties in mathematics, especially regarding the simplification of complex problems where perpendicularity in higher dimensions plays a significant role.