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"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?

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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.

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  • $\begingroup$ Thank you very much. That was it, I didn't understand the expression properly. $\endgroup$ – Windy Dec 8 '18 at 9:24
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Here's my understanding of the problem:

enter image description here

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

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

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