There is this problem I am trying to solve –

“The position vectors of points A and B relative to the origin are 3i+2j-k adn 5i+6j+5k respectively. Find the position vector of the point P which lies on AB produced such that AP=3BP.”

Actually I can solve it, provided I find where P lies – on AB line sector or the continuation of AB. That’s exactly what I don’t understand – how to visualize the problem.

**Could you please help me understand, how do I figure out where exactly P lies?**

Thank you very much in advance.