Edexcel IGCSE Math A 5.1.HF resultant vectors

Practise resultant-vector questions by following paths through the diagram, adding vector steps and simplifying coefficients of a and b.

Exam points

Find a resultant vector by adding or subtracting directed vector steps.
Simplify expressions in a and b after following a path through the diagram.
Use midpoint, ratio or regular-hexagon information when forming the vector.

[Maximum number: 2]

OAB is a triangle.

Figure for Question 5.1.HF Resultant vectors question 1 — Edexcel IGCSE Math A Higher

$\overrightarrow{OA}=4\mathbf a$ $\overrightarrow{OB}=4\mathbf b$ P is the point on AB such that AP:PB=1:3

Express $\overrightarrow{OP}$ in terms of $\mathbf a$ and $\mathbf b$
Give your answer in its simplest form.

\overrightarrow{AB}=-4\mathbf a+4\mathbf b

\overrightarrow{OP}=4\mathbf a+\frac14\overrightarrow{AB}

\overrightarrow{OP}=4\mathbf a+\frac14(-4\mathbf a+4\mathbf b)=3\mathbf a+\mathbf b

Final answer:

3\mathbf a+\mathbf b

M1ft for a correct expression following through their part (a), where $\overrightarrow{AB}$ is of the form $m\mathbf a+n\mathbf b$ , $m,n\ne0$ .
A1; allow $\mathbf b+3\mathbf a$ .

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5.1.HF Resultant vectors question 1