Position-And-Displacement-Vectors Edexcel Higher

Position & displacement vectors

What are position vectors?

• A position vector describes where a specific point, A , is, relative to a fixed origin, O

  • Lower-case bold (or underlined) letters are used

    • The point A has position vector a = 

• Their components are equal to their coordinates

  • The point with coordinates (3, -2) has position vector from the origin

What are displacement vectors?

• A displacement vector describes the direction and distance between two points

  • The displacement vector from A  to B  is 

    • How to get from A to B

• If the points A  and B  have position vectors a and b relative to O 

  • then A to B  is the same as A  to O  (-a) followed by O  to B  (b)

    • <img alt=”stack A B with rightwards arrow on top equals negative bold a plus bold b equals bold b minus bold a” data-mathml='<math ><semantics><mrow><mover accent=”true”><mrow><mi>A</mi><mi>B</mi></mrow><mo>&#8594;</mo></mover><mo>=</mo><mo>-</mo><mi mathvariant=”bold”>a</mi><mo>+</mo><mi mathvariant=”bold”>b</mi><mo>=</mo><mi mathvariant=”bold”>b</mi><mo>-</mo><mi mathvariant=”bold”>a</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”26″ role=”math” 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