CAIE A Level Mathematics 9709 · Vectors

Vectors: calculation question

3 marksChallenge

Points $A$ and $B$ have position vectors $\overrightarrow{OA} = 6\mathbf{i} - 3\mathbf{j}$ and $\overrightarrow{OB} = 10\mathbf{i} - 3\mathbf{j}$ . The point $P$ lies on $AB$ so that $AP : PB = 1 : 3$ .

(a)
Find the $\mathbf{i}$ -component of the position vector of $P$ .
[3]

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Vectors: calculation question

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