Mathematics 0580 · IGCSE · Vector geometry

Vector geometry — practice question

Triangle ABC is given, with B at $(1,-10)$, A at $(4,14)$ and $\overrightarrow{CA} = \begin{pmatrix}-11\\8\end{pmatrix}$.
(a(i))[2]

Find the coordinates of C from the information given.

(a(ii))[1]

Find $\overrightarrow{BA}$ in component form.

(a(iii))[2]

Find the value of $|\overrightarrow{CA}|$.

(b(i))[3]

Show that $\overrightarrow{OR} = \frac{2}{5}a + \frac{3}{5}b$ from the given setup.

(b(ii)(a))[4]

$\overrightarrow{NT} = 4a + kb$ and $\overrightarrow{OT} = c\overrightarrow{OR}$. Find the values of $k$ and $c$.

(b(ii)(b))[1]

Find the vector $\overrightarrow{MT}$.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Right $x$-coordinate: $15$

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