Final answer:
The angle between two vectors X and Y, given their equal dot products (X.Y = Y.X), can range from 0° to 180°. If vectors are perpendicular, this angle is 90 degrees, but the exact angle cannot be determined without more information.
Step-by-step explanation:
If X.Y equals Y.X, where X and Y represent vectors, and the dot product of the two vectors is equal, then the angle between them can be found using the dot product formula. The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them, symbolized as A · B = AB cos(θ). Given that X and Y are interchangeable in the dot product (due to its commutative property), the angle between them can be calculated by rearranging the formula to solve for the angle, such as using the inverse cosine function:
θ = cos-1(X.Y / (|X||Y|))
However, the equation provided does not indicate an inequality or a specific value for the dot product, implying that the angle could range from 0° to 180° assuming the vectors are non-zero. In cases where vectors are perpendicular to each other, as hinted by the right triangle example, the angle between them is 90 degrees. Still, without more information, we can't determine the exact angle between vectors X and Y.