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Vectors (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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Cards in this collection (15)

  • What is a vector?

    A vector is a type of number with both size and direction.

    A vector with its magnitude and direction labelled.

  • True or False?

    stack B A with rightwards arrow on top represents the vector from B to A.

    True.

    stack B A with rightwards arrow on top represents the vector from B to A.

  • How do you write "3 to the left and 2 up" as a column vector?

    "3 to the left and 2 up" can be written as the column vector open parentheses table row cell negative 3 end cell row 2 end table close parentheses.

  • True or False?

    The vector open parentheses table row 2 row 3 end table close parentheses must be drawn starting at open parentheses 0 comma space 0 close parentheses and ending at the point open parentheses 2 comma space 3 close parentheses.

    False.

    The vector open parentheses table row 2 row 3 end table close parentheses does not need to be drawn starting at open parentheses 0 comma space 0 close parentheses and ending at the point open parentheses 2 comma space 3 close parentheses.

    The vector can start at any point, as long as it goes 2 to the right and 3 up.

  • How do you add two column vectors?

    To add two column vectors, add together the numbers in the corresponding parts of the vector.

    For example, open parentheses table row 1 row 2 end table close parentheses plus open parentheses table row 3 row cell negative 5 end cell end table close parentheses equals open parentheses table row cell 1 plus 3 end cell row cell 2 plus open parentheses negative 5 close parentheses end cell end table close parentheses equals open parentheses table row 4 row cell negative 3 end cell end table close parentheses.

  • True or False?

    5 cross times open parentheses table row 3 row 4 end table close parentheses equals open parentheses table row 15 row 4 end table close parentheses

    False.

    5 cross times open parentheses table row 3 row 4 end table close parentheses not equal to open parentheses table row 15 row 4 end table close parentheses.

    To multiply a vector by a scalar, you need to multiply all parts of the vector by the scalar.

    5 cross times open parentheses table row 3 row 4 end table close parentheses equals open parentheses table row cell 5 cross times 3 end cell row cell 5 cross times 4 end cell end table close parentheses equals open parentheses table row 15 row 20 end table close parentheses.

  • If you know what the vectors bold a and bold b look like, how can you draw the vector bold a plus bold b?

    If you know what the vectors bold a and bold b look like, to draw the vector bold a plus bold b:

    • Draw the vector bold a

    • Draw the vector bold b starting at the end of bold a

    • Draw a vector from the start of bold a to the end of bold b

    An arrow representing vector a has an arrow representing vector b starting from its end point. The resultant vector, a + b is drawn as an arrow that starts from the start point of vector a and ends at the end point of vector b.

  • True or False?

    The vector 2 bold a is in the same direction as bold a but is double the length of bold a.

    True.

    The vector 2 bold a is in the same direction as bold a but is double the length.

    Scalar multiples of a vector change the length of the vector.

  • What is the geometrical relationship between the vectors bold a and negative bold a?

    The vectors bold a and negative bold a have the same length but they are in opposite directions.

  • Define a vector path.

    A vector path is a route made of vectors that takes you from a start point to an end point.

    On a grid the route runs along the sides of the shapes, and the answer is written in terms of the vectors you have been given.

  • On a grid of identical parallelograms with \mathbf{a} and \mathbf{b} marked, how do you write the vector between two points?

    Count how many moves along \mathbf{a} and how many along \mathbf{b} the route takes, choosing the route with the fewest moves.

    Those counts become the multiples in the answer, so three moves along \mathbf{a} and two along \mathbf{b} give 3 \mathbf{a} + 2 \mathbf{b}.

  • What happens to a term when the route travels against the direction of \mathbf{a}?

    It takes a minus sign, so one move backwards along \mathbf{a} contributes - \mathbf{a}.

    Four such moves contribute - 4 \mathbf{a}.

  • A route from G to T runs twice along \mathbf{b} and then three times along \mathbf{a}. Complete the result:

    \overset{\rightarrow}{G T} = \_\_\_\_\_\_ \mathbf{a} + \_\_\_\_\_\_ \mathbf{b}

    The completed result is:

    \overset{\rightarrow}{G T} = 3 \mathbf{a} + 2 \mathbf{b}

    The number of moves along each vector becomes its multiple, and the order in which they are walked does not change the answer.

  • True or False?

    Two different routes between the same two points give different vectors.

    False.

    Any route from one point to the other simplifies to the same vector.

    The route is only a way of counting the moves, and it is the start and end points that fix the result.

  • If \overset{\rightarrow}{F B} = \mathbf{a} - \mathbf{b}, what is \overset{\rightarrow}{B F}?

    It is \mathbf{b} - \mathbf{a}, the negative of the original.

    Reversing a route reverses every move along it, so every sign flips.

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