A-level · Vectors

Vector notation and representationExam-style questions

What a vector is (a size and a direction), the ways we write one (bold letter, arrow, column, i–j components), and how to add, subtract and scale vectors — both geometrically (nose-to-tail) and component by component.

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3 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3

1
Given $\mathbf{a} = 2\mathbf{i} - \mathbf{j} + 3\mathbf{k}$ and $\mathbf{b} = \mathbf{i} + 4\mathbf{j} - 2\mathbf{k}$ , find $\mathbf{a} + \mathbf{b}$ and $\mathbf{a} - \mathbf{b}$ .
Level 2 · 2 marksTry it
2
Find the value of $t$ for which $6\mathbf{i} + t\mathbf{j} + 9\mathbf{k}$ is parallel to $2\mathbf{i} - \mathbf{j} + 3\mathbf{k}$ .
Level 3 · 2 marksTry it
3
Given $\mathbf{a} = \mathbf{i} + 2\mathbf{j} - 2\mathbf{k}$ and $\mathbf{b} = 5\mathbf{i} - 2\mathbf{j} + 4\mathbf{k}$ , find $3\mathbf{a} - 2\mathbf{b}$ and the vector $\mathbf{c}$ for which $\mathbf{a} + 2\mathbf{c} = \mathbf{b}$ .
Level 3 · 4 marksTry it