CAIE IGCSE Mathematics Extended Expressing Vectors

Practise following directed paths and combining two coplanar base vectors to express position and displacement vectors in their simplest form.

Exam points

choose a valid route between the named points and add each directed vector with the correct sign
convert midpoint or section-ratio information into a fractional multiple of a known vector
collect coefficients of the two base vectors and present the requested vector in simplest form

[Maximum number: 2]

Figure for Question E7.4.3 Use the sum and difference of two or more vectors to express given question 1 — CAIE IGCSE Mathematics Extended

$\overrightarrow{O T}=\mathbf{t}, \overrightarrow{O U}=\mathbf{u}$ and U Y=2 Y T.

Find $\overrightarrow{O Y}$ in terms of t and u.

Give your answer in its simplest form.

\overrightarrow{O Y}=

$\overrightarrow{OY}=\frac{2}{3}\mathbf{t}+\frac{1}{3}\mathbf{u}=\frac{1}{3}(2\mathbf{t}+\mathbf{u})$

M1 for $\overrightarrow{UY}=\frac{2}{3}(\mathbf{t}-\mathbf{u})$ oe or $\overrightarrow{TY}=\frac{1}{3}(\mathbf{u}-\mathbf{t})$ oe or correct route soi

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E7.4.3 Use the sum and difference of two or more vectors to express given question 1