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

Question id: 323. This question is similar to one that appeared on a GCSE Higher paper in 2017. The use of a calculator is not allowed.

In the parallelogram OABC two of the sides can be represented by vectors \(a\) and \(c\).

\( \overrightarrow{OA} = a \) and \( \overrightarrow{OC} = c \)

\( X \) is the midpoint of the line \( AC \).

\( OCD \) is a straight line such that \(OC:CD = k:1 \)

Given that \( \overrightarrow{XD} = 3c - \frac12 a \) find the value of \( k \).

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