Mathematics 4024 · O Level · Vectors in two dimensions

Vectors in two dimensions — practice question

The diagram displays the vectors $\vec{PQ}$ and $\vec{QR}$. $\vec{PQ} = \begin{pmatrix}5 \\ 2\end{pmatrix}$ and $\vec{QR} = \begin{pmatrix}a \\ b\end{pmatrix}$.
(a(i))[2]

Find the values of $a$ and $b$.

(a(ii))[2]

Calculate the magnitude of $\vec{PQ}$.

(b(i))[1]

Express $\vec{CE}$ in the simplest possible form, in terms of $a$ and $b$.

(b(ii))[1]

Express $\vec{OE}$ in the simplest possible form, in terms of $a$ and $b$.

(b(iii))[2]

A point $F$ lies on $BC$ with $\vec{OF} = k\vec{OE}$. Find $BF : FC$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: $a=1,\ b=-3$

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