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"`.

Answer 1

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"`