CAIE IGCSE Additional Math 13.2 Use Position and Unit Vectors Questions

Practise normalising two-dimensional vectors, calculating their magnitudes and expressing directions in component or i, j form with Cambridge International Additional Mathematics questions.

Exam points

Find a unit vector by dividing a vector by its magnitude, and express direction vectors in component or i, j form.

[Maximum number: 3]

The point O is the origin.
Two points P and Q are such that $\overrightarrow{PQ}$ is in the same direction as $-\mathbf{i}+5\mathbf{j}$ .

The point R is such that $\overrightarrow{OR}$ is in the same direction as $\overrightarrow{PQ}$ and the magnitude of $\overrightarrow{OR}$ is $3\sqrt{26}$ .
Find $\overrightarrow{OR}$ .

$[\overrightarrow{OR}=]k(-\mathbf{i}+5\mathbf{j})$ or $k\binom{-1}{5}$
B1 soi
$\sqrt{1^2+5^2}=\sqrt{26}$
B1 for finding the magnitude of $\overrightarrow{PQ}$ ;
allow unsimplified.
$-3\mathbf{i}+15\mathbf{j}$ or $\binom{-3}{15}$
B1
Allow $3(-\mathbf{i}+5\mathbf{j})$ or $3\binom{-1}{5}$ . Do not isw.

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CAIE IGCSE Additional Math 13.2 Use Position and Unit Vectors Questions question 1