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Question id: 200. This question is similar to one that appeared in a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

Consider a triangle ABC where M is the midpoint of AB and F is the point on BC where BF:FC = 3:4.

(a) If \(\overrightarrow{AB}=b\) and \(\overrightarrow{AC}=c\) work out \(\overrightarrow{MF}\) in terms of \(b\) and \(c\) giving your answer in its simplest form.

(b) Use your answer to part (a) to explain whether MF is parallel to AC or not.

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