A position vector is the vector of an arrow drawn to from an origin to a point. Look at the example below - a Cartesian plane in which we see points AA A and BB B The position vector of AA A connects the origin, marked OO O , to AA A - it can be written as a⃗ a→ \vec a or OA→OA→ \vec{OA} . Similarly, the position vector of B connects the origin to BB B - it can be written as b⃗ b→ \vec b or OB→OB→ \vec{OB} It is important that the letters are written in this order. The vector BO→BO→ \vec{BO} would connect B to the origin and therefore represents −b⃗ −b→ -\vec b . If you are using Cartesian components to describe a position vector, the Cartesian coordinates of a point can be used to describe the position vector of that point. For example, AA A has the coordinates (1,4)(1,4) (1,4) . This means its position vector can be written as a⃗ =a→= \vec a=1ı⃗ +4ȷ⃗ 1ı→+4ȷ→ 1 \vec{\imath} + 4 \vec{\jmath} or a⃗ =[14]a→=[14] \vec a= [14]
Position vectors can be used to describe the vector between two points. The position vector →AB goes from A to B Going from A to B is the same as going from A to O and then from O to B Therefore, →AB=→b−→a This means that the component form of →AB can be found by subtracting the components of A from B, i.e. →AB=→b−→a
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