Final answer:
To find the angle between vectors A and B, we need to use the cosine formula and the given equation ABˉCˉ=0. Solving the equation and analyzing the cosine formula, we find that the angle between Aˉ and Bˉ is 90 degrees. Option (D) is correct.
Step-by-step explanation:
To find the angle between vectors A and B, we need to use the cosine formula which states:
A•B = |A||B|cos(θ), where A•B is the dot product of A and B, |A| and |B| are the magnitudes of A and B, and θ is the angle between A and B. From the given equation ABˉCˉ=0, we can rewrite it as AB•C = 0. Substituting the values, we have |A||B||C|cos(θ) = 0. Since |A|, |B|, and |C| are all non-zero, cos(θ) = 0, which occurs when θ = 90 degrees. Therefore, the angle between Aˉ and Bˉ is D. 90 degrees.
The definition of perpendicular relies on the angle between the vectors being 90 degrees, and with the zero vector, there's no intuitive way of thinking about the angle. The orthogonal case deals with the zero vector, and it is orthogonal to every vector because the zero vector dotted with anything is zero.