"The position vectors of points $A$ and $B$ relative to the origin are $3i+2j-k$ and $5i+6j+5k$ respectively. Find the position vector of the point $P$ which lies on $AB$ produced such that $AP=3BP$."
Actually I can solve this, 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.
How do I figure out where exactly $P$ lies?