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Flashcards · Maths · Vectors, Constructions and Loci

Column Vectors and Vector Arithmetic

16 cards

  1. What is a vector?

    A quantity with a size and a direction, such as a movement.

  2. What does the top number of a column vector show?

    The horizontal move, right if positive.

  3. What does the bottom number of a column vector show?

    The vertical move, up if positive.

  4. What does \(\overrightarrow{AB}\) mean?

    The vector from \(A\) to \(B\).

  5. What is \(\overrightarrow{BA}\) in terms of \(\overrightarrow{AB}\)?

    \(-\overrightarrow{AB}\).

  6. How do you find a vector from two coordinates?

    Subtract the coordinates of the start from the end.

  7. How do you add column vectors?

    Add the top numbers and add the bottom numbers.

  8. How do you subtract column vectors?

    Subtract the top numbers and subtract the bottom numbers.

  9. How do you multiply a vector by a number?

    Multiply both numbers in the column by it.

  10. When are two vectors equal?

    When they have the same size and direction.

  11. When are two vectors parallel?

    When one is a multiple of the other.

  12. What does a negative multiple of a vector do?

    It points in the opposite direction.

  13. How do you draw \(\mathbf{a} + \mathbf{b}\)?

    Draw \(\mathbf{b}\) starting from the end of \(\mathbf{a}\), then join the start to the finish.

  14. How do you draw \(\mathbf{a} - \mathbf{b}\)?

    Add \(\mathbf{a}\) and \(-\mathbf{b}\).

  15. How do you find the length of a column vector?

    Use Pythagoras' theorem on the two numbers (Higher tier).

  16. What is the length of \(\begin{pmatrix} 3 \\ 4 \end{pmatrix}\)?

    5 (Higher tier).