Final answer:
The component of B along the direction of A and the component of A along the direction of B are both zero because orthogonal vectors are perpendicular, resulting in a dot product of 0. The magnitude of A cannot be established from this information alone.
Step-by-step explanation:
Understanding Orthogonal Vectors
If vectors A and B are orthogonal, they are perpendicular to each other. The component of B along the direction of A and the component of A along the direction of B would both be zero because in the dot product, A · B = |A||B|cosθ, the angle θ is 90 degrees, so cosθ is 0, resulting in a dot product of 0. Hence, the magnitude of the orthogonal component of either vector in the direction of the other is zero.
Since vectors A and B are orthogonal, the component of B along the direction of A is 0, and similarly, the component of A along the direction of B is also 0. This satisfies the property of orthogonal vectors, where their scalar product equals 0.
Concerning magnitudes, the magnitude of a vector is not dependent on its direction but rather on the lengths of its components. In this case, knowing the magnitude of A or B is not possible without additional information, even if we know they are orthogonal.