Final answer:
The problem is missing the necessary context or additional information which is required to find the lengths of BQ, OP, and OQ in triangle ABC. Without such information, the problem cannot be accurately solved.
Step-by-step explanation:
The student's question is about finding lengths of segments BQ, OP, and OQ within triangle ABC. However, the provided information and the way the problem is stated seem to be incomplete or lacking context. Specific relationships or additional data are required to find the lengths using geometric principles or vector operations. Without the necessary context, such as the positions of points P, Q, O, and how they relate to triangle ABC, or any additional geometric properties or vector information, it's not possible to accurately determine these lengths.
In mathematics, when handling geometry problems, it is essential to have clear definitions of the points involved and their relationships to each other in order to apply the correct theorems, laws, or formulae to find the answer.