-- Vectors - PureMaths 3 - RP AS & A Level Mathematics

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    3.7 Vectors
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     Video transcript

    Welcome to this short insights video to help your learners better understand vector equations.
    
    One of the challenges for learners working with vector equations is grasping the difference between regular equations, using Cartesian coordinates, and vector equations to describe lines.
    
    Learners are used to expressing lines in terms of cartesian x and y points.
    
    However, vectors are described differently. They have two components..
    
    …a starting point and a direction component.
    
    They understand what this cartesian equation for a line will look like…
    
    ...Where the m term is the gradient or incline of the line and c acts like an offset to the y crossing point.
    
    But a vector equation for a line is described like this…
    
    ...This line starts at cartesian point x one, y one then travels ‘towards’ cartesian point x two, y two. And the t function describes the fact that the line will continue in that direction forever.
    
    Which is quite different as they have a cartesian point to start from, but the second component, direction is expressed using a point the line goes through but continues for all values of t.
    
    For example...
    
    This line starts at cartesian point x equals two, y equals minus one in terms of x and y coordinates, but then travels ‘towards’ cartesian point x equals one, y equals five.
    
    Once this transformation from cartesian space to vector space is understood transforming back to Cartesian space becomes much easier. We now know that for any point on the line…
    
    x equals 2 plus one times t
    
    And
    
    Y equals minus 1 plus five times t.
    
    Then, for any value of t in vector space we can know what the values for x and y will be in Cartesian space.
    
    Then learners can take this concept forward, looking at more than one equation, to see where vector lines cross by finding out where the vector equations are equal to each other.
    
    So, I hope this short insights video has been useful to you to help your learners better understand vector equations.
    
    Thank you.
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