{"id":"vector-angle","version":"1.0.0","description":"Compute the angle in radians between two equal-length finite-number vectors.","supported_operations":["angle between vectors","vector angle radians"],"unsupported_operations":["angle in degrees (convert the radian result separately)","angle for a zero-magnitude vector"],"semantics":["Inputs a and b are arrays of finite JSON numbers with the same length, from 1 to 64 entries, magnitude bounded to at most 1000000.","The angle is acos((a . b) / (|a| * |b|)), computed in IEEE-754 double precision and returned in radians in the closed range [0, pi].","The cosine argument is clamped to [-1, 1] before acos to compensate for floating-point rounding that could otherwise push it slightly outside that range.","Either vector having Euclidean norm 0 makes the angle undefined and is rejected."],"limits":{"max_dim":64,"max_abs_value":1000000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["a","b"],"properties":{"a":{"type":"array","minItems":1,"maxItems":64,"items":{"type":"number"}},"b":{"type":"array","minItems":1,"maxItems":64,"items":{"type":"number"}}}},"output_schema":{"type":"object","additionalProperties":false,"required":["result"],"properties":{"result":{"type":"number"}}},"examples":[{"input":{"a":[1,0],"b":[0,1]},"output":{"result":1.5707963267948966}}],"execute_url":"/v1/tools/vector-angle/versions/1.0.0/execute"}