Finding a vector position

Question

"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?

Answer 1

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.

Hope it is helpful.

Answer 2

Here's my understanding of the problem:

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