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# P3 Vector watch

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1. 2 points A and B have position vectors and b respectively. show that the point which divides AB internally in the ratio m:n has the position vector:

(na + mb)/(n+m)

now I know why it's n+m at the bottom, but why is it na or mb at the top, can it be ma + nb instead?
2. Not if the ratio is m:n.
3. I still don't get why it's na + mb
4. Suppose that the point is K, then:
OK = OA + AK
= a + (m/m+n)AB
= a + (m/m+n)(b-a)
= a + mb/(m+n) - am/(m+n)
= (am + an + mb - am)/(m+n)
= (na + mb)/(m+n)
5. Thanks a lot for that

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