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Examples for Division of a line segment

Example 1

Given two points P1 and P2 in space find the point R dividing the line segment P1P2 in the ratio -2 : 1. Top of page

Solution

If R divides P1P2 in the ratio -2 : 1 then -P--->R 1 = -2-P--->R 2.
P1 P2 R O

The position vector ---> OR is then equal to

----> ----> -O-->R = 1OP1----2OP2--= - -O-P--> + 2-O-P--> . - 2 + 1 1 2