GCSE · Vectors

Vector proofsExam-style questions

What a vector equation actually proves — a scalar multiple gives parallel and nothing more, a multiple plus a shared point gives collinear — and how to write the conclusion in the form a mark scheme rewards.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
$P$ , $Q$ , $R$ and $S$ are four points. $\overrightarrow{PQ} = 2\mathbf{a} + 6\mathbf{b}$ and $\overrightarrow{RS} = 3\mathbf{a} + 9\mathbf{b}$ .

(a) Show that $PQ$ is parallel to $RS$ .

(b) Freya says: "This working also proves that $P$ , $Q$ , $R$ and $S$ all lie on the same straight line."

Freya is wrong. Explain why.
Level 3 · 3 marksTry it
2
$A$ , $B$ and $C$ are three points.

$\overrightarrow{AB} = 4\mathbf{a} - 2\mathbf{b}$ and $\overrightarrow{BC} = 10\mathbf{a} - 5\mathbf{b}$ .

Prove that $A$ , $B$ and $C$ are collinear.
Level 3 · 3 marksTry it