Mathematics 4024 · O Level · Vectors in two dimensions

Vectors in two dimensions — practice question

The displacement vector is $\vec{AB} = \begin{pmatrix} -3 \\ 5 \end{pmatrix}$.
(a(i))[2]

Calculate the length $|\vec{AB}|$.

(a(ii)(a))[1]

$\vec{AC} = \begin{pmatrix} 6 \\ 2 \end{pmatrix}$ and $C$ is the point $(10, -1)$. Find the coordinates of $A$.

(a(ii)(b))[2]

B is the midpoint of $AD$. Find the coordinates of $D$.

(b(i))[1]

The diagram is triangle $OPQ$. $\vec{OP} = \vec{p}$ and $\vec{OQ} = \vec{q}$. $R$ lies on $OQ$ so that $OR = 2RQ$. $S$ is the midpoint of $PQ$. Express, as simply as possible, in terms of $\vec{p}$ and/or $\vec{q}$, $\vec{PQ}$.

(b(ii))[2]

Express $\vec{OS}$ using $\vec{p}$ and/or $\vec{q}$.

(b(iii))[2]

Express $\vec{SR}$ using $\vec{p}$ and/or $\vec{q}$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: The answer is $5.83$.

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