# 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.

Hope it is helpful.

• Thank you very much. That was it, I didn't understand the expression properly. – Windy Dec 8 '18 at 9:24

Here's my understanding of the problem:

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

• P lies on AB produced and not on AB as you are assuming. – Martund Dec 8 '18 at 9:35
• What does "AB produced" mean? – David G. Stork Dec 8 '18 at 11:40
• Means that you have to extend AB to get P on that, it is not on line segment AB. – Martund Dec 8 '18 at 11:46
• "AB produced" is not standard English. – David G. Stork Dec 8 '18 at 11:48