Finding-Vector-Paths Aqa Higher

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” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2226%22%20width%3D%2277%22%20wrs%3Abaseline%3D%2220%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%26%23×2192%3B%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%20mathvariant%3D%22bold%22%3Ea%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%20mathvariant%3D%22bold%22%3Eb%3C%2Fmi%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’horizontal225a4f6397f19c438fc1d’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMlJxIOAAAADMAAAATmNtYXCwg0j%2FAAABHAAAAERjdnQgAAcAAAAAAWAAAAACZ2x5ZuwE1kUAAAFkAAAA3GhlYWQNciGiAAACQAAAADZoaGVhBusXCAAAAngAAAAkaG10eGjtB6sAAAKcAAAAEGxvY2EAAYSYAAACrAAAABRtYXhwBLEEbgAAAsAAAAAgbmFtZReja%2F8AAALgAAAByXBvc3QB9wD6AAAErAAAACBwcmVwu5WEAAAABMwAAAAHAAACRwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAACOv8xEDev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEADAAAAAIAAgAAgAAI6%2FyAPIL%2F%2F8AACOv8gDyC%2F%2F%2F3FIOAg34AAEAAAAAAAAAAAAHAAAAAQAAAVUBqwGrAAMAIxgBsAQQsAE8sAEQsALUsAIQsAU8ALAEELAB1LABELAA1DAxERUhNQGrAatWVgABAAAAqwErAlUACABBGAGwCRCwA9SwAxCwAtSwAhCwBTywCRCwBzwAsAkQsAfUsAcQsAjUsAgQsAHUsAEQsALUsAcQsAXUsAUQsATUMDETJzUNATU3IzVgYAEr%2FtVgYAGqQGvV1WpAVgABAIEBVgGsAawAAwAdGAGwBRCwADywABCwAdQAsAUQsADUsAAQsAPUMTABITUhAaz%2B1QErAVZWAAEAAAABAABFUxdzXw889QADBAD%2F%2F%2F%2F%2F1a3u0f%2F%2F%2F%2F%2FVre7RAAAAAAMAAwAAAAAKAAIAAQAAAAAAAQAAA%2Bj%2FagAAF3AAAP%2F%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%2FwACjYUA)format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-st