The vector \(\binom{6}{k}\) is parallel to the vector \(\binom{2}{-5}\). Find the value of \(k\).
Question 1 Report
The vector \(\binom{6}{k}\) is parallel to the vector \(\binom{2}{-5}\).
Find the value of \(k\).
Answer Details
Two vectors are parallel exactly when one is a scalar multiple of the other, which means both components are multiplied by the same number.
- Compare the top components to find the scale factor: \(6\div2=3\) [M1]
- The same factor must apply to the bottom components: \(k=3\times(-5)=-15\) [A1]
The single scale factor is the whole point. Choosing \(k=-5\) treats the components as unrelated, and adding \(4\) to each component (since \(6=2+4\)) would be a translation of the vector, not a scalar multiple, so it does not preserve direction. A quick check is that \(\binom{6}{-15}=3\binom{2}{-5}\).
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