Mathematics 4024 · O Level · Vectors in two dimensions

Vectors in two dimensions — practice question

From the diagram, $\vec{OB} = \begin{pmatrix}12\\6\end{pmatrix}$.
(a)[1]

Show that the gradient of $OB$ equals $\frac{1}{2}$.

(b(i))[1]

As $AP$ is parallel to $OB$ and $\vec{AP} = \begin{pmatrix}p\\2\end{pmatrix}$, find the value of $p$.

(b(ii))[1]

Write down the ratio $\dfrac{AP}{OB}$.

(c(i))[1]

$AQ$ is perpendicular to $OB$. Write down the gradient of $AQ$.

(c(ii))[1]

With $\vec{AQ} = \begin{pmatrix}3\\q\end{pmatrix}$, find the value of $q$.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Gradient is $\frac{6}{12}$

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