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

Question id: 234. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

In the diagram above (not drawn to scale) \(X\) is the point on \(AB\) such that \(AX:XB = 9:4\).

The position vector of \(A\) is \(3a\) and the position vector of \(B\) is \(3b\).

Find the value of \(k\) if \(\vec{OX} = k(4a + 9b)\) where \(k\) is a scalar quantity.

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