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Question
The points A, B, C have position vectors `bar"a", bar"b" and bar"c"` respectively. The point P is the midpoint of AB. Find the vector `bar"PC"` in terms of `bar"a", bar"b", bar"c"`.
Solution
P is the mid-point of AB.
∴ `bar"p" = (bar"a" + bar"b")/2, "where" bar"p"` is the position vector of P.
Now, `bar"PC" = bar"c" - bar"p" = bar"c" - 1/2(bar"a" + bar"b")`
`= -1/2(bar"a" + bar"b") + bar"c"`
`= - 1/2 bar"a" - 1/2 bar"b" + bar"c"`
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