# Finding a vector position

"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?

Since it is written that "point P which lies on AB produced", therefore P doesn't lie on line AB and given is the case of external division.

Apply the external section formula directly.

The point $$P$$ is at $$A + 3/4 (B-A)$$.