In the diagram, $$\(O\)$$ is the origin, $$\(O T=2 T D\)$$ and $$\(M\)$$ is the midpoint of $$\(T C\)$$. $$\(\overrightarrow{O C}=\mathbf{c}\)$$ and $$\(\overrightarrow{O D}=\mathbf{d}\)$$. Find the position vector of $$\(M\)$$. Give your answer in terms of $$\(\mathbf{c}\)$$ and $$\(\mathbf{d}\)$$ in its simplest form. .............................................

Mathematics
IGCSE&ALevel
CAIE
Exam No:0580_s20_qp_42 Year:2020 Question No:2(d)

Answer:

\(\frac{1}{2} \mathbf{c}+\frac{1}{3} \mathbf{d}\)

Knowledge points:

E7.3.1 Calculate the magnitude of a vector
E7.3.2    Represent vectors by directed line segments. (In their answers to questions, candidates are expected to indicate a in some definite way
E7.3.3 Use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors.
E7.3.4 Use position vectors.

Solution:

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