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Flashcards · Maths · Vectors, Constructions and Loci

Vector Geometry and Proof

16 cards

  1. If \(\overrightarrow{OA} = \mathbf{a}\) and \(\overrightarrow{OB} = \mathbf{b}\), what is \(\overrightarrow{AB}\)?

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

  2. What is \(\overrightarrow{AO}\) in terms of \(\overrightarrow{OA}\)?

    \(-\overrightarrow{OA}\).

  3. How do you find the vector to the midpoint of \(AB\)?

    \(\overrightarrow{OM} = \overrightarrow{OA} + \dfrac{1}{2}\overrightarrow{AB}\), which is \(\dfrac{1}{2}(\mathbf{a} + \mathbf{b})\).

  4. What fraction of \(AB\) is \(AP\) when \(AP : PB = 3 : 1\)?

    \(\dfrac{3}{4}\).

  5. How do you find the vector to a point on \(AB\)?

    Go to \(A\), then add the fraction of \(\overrightarrow{AB}\) to reach the point.

  6. When are two vectors parallel?

    When one is a multiple of the other.

  7. How do you prove lines are parallel?

    Show that their vectors are multiples of each other.

  8. When are three points collinear?

    When two of the vectors between them are parallel and share a point.

  9. What do you write at the end of a collinear proof?

    The vectors are parallel and share a point, so the points are on a straight line.

  10. What does \(\overrightarrow{AB} = 2\overrightarrow{BC}\) show?

    \(A\), \(B\) and \(C\) are on a straight line, with \(AB\) twice as long as \(BC\).

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

    \(\sqrt{x^2 + y^2}\).

  12. What is the length of \(\begin{pmatrix} 5 \\ 12 \end{pmatrix}\)?

    13.

  13. Why choose a route using known vectors?

    You can add them to reach any point.

  14. How should you simplify a vector expression?

    Collect the terms in each letter.

  15. What is the opposite of \(\mathbf{a} - \mathbf{b}\)?

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

  16. Why draw a diagram in a vector question?

    It shows which vectors are known and which route to use.