CAIE IGCSE Additional Math 13.2 position and unit vectors

Use this position-and-unit-vectors page to find vector magnitudes, divide components by length and state directions in column or i-j form.

Exam points

Find the magnitude of a vector before forming the corresponding unit vector.
Write unit vectors in column form or i-j form with correctly scaled components.
Use coordinates or position-vector notation to describe a point or direction.

[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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13.2. Use position and unit vectors question 1