Finding Vector Paths (AQA GCSE Maths: Foundation): Revision Note

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, you need to find the route which uses the least number of moves

  • 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 up and 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. $\overrightarrow{AR}=2\mathbf{a}+3\mathbf{b}$

• 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. $\overrightarrow{FB}=-\mathbf{b}+\mathbf{a}$ or $\overrightarrow{FB}=\mathbf{a}-\mathbf{b}$

    • Likewise, $\overrightarrow{BF}=-\overrightarrow{FB}=-\left(-\mathbf{b}+\mathbf{a}\right)=\mathbf{b}-\mathbf{a}$

• It is possible to describe any vector that goes from one point to another in the above diagram in terms of a and b