Finding-Vector-Paths Aqa Foundation

Finding vector paths

How do I find the vector between two points?

• A vector path is a path of vectors taking you from a start point to an end point

• The following grid is made up entirely of parallelograms

  • The vectors a and b defined as marked in the diagram:

    • Any vector that goes horizontally to the right along a side of a parallelogram will be equal to a

    • Any vector that goes up diagonally to the right along a side of a parallelogram will be equal to b

• To find the vector between two points

  • Count how many times you need to go horizontally to the right

    • This will tell you how many a‘s are in your answer

  • Count how many times you need to go up diagonally to the right

    • This will tell you how many b‘s are in your answer

  • Add the a‘s and b‘s together

    • E.g. 

• You will have to put a negative in front of the vector if it goes in the opposite direction

  • –a is one length horizontally to the left

  • –b is one length down diagonally to the left

    • E.g.  or <img alt=”stack F B with rightwards arrow on top equals bold a minus bold b” data-mathml=”<math ><semantics><mrow><mover><mrow><mi>F</mi><mi>B</mi></mrow><mo>&#8594;</mo></mover><mo>=</mo><mi mathvariant=”bold”>a</mi><mo>-</mo><mi mathvariant=”bold”>b</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” height=”26″ role=”math” 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