## Exam-Style Question on Vectors## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 527. This question is similar to one that appeared on a GCSE Higher paper in 2019. The use of a calculator is allowed.

ABCD is a quadrilateral

\(\overrightarrow{AB} = p\)

\(\overrightarrow{BC} = q\)

\(\overrightarrow{CD} = 2q - p\)

(a) Express \(\overrightarrow{AD}\) in terms of \(p\) and/or \(q\) giving your answer in its simplest form.

E is the midpoint of AB.

F is the point on DE such that DF : FE = n : 1

AFC is a straight line.

(b) Work out the value of n.

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