BonBon2
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http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf

when doing this paper, for question 4 a i got a value of -10,15,-5 for the direction vector of the equation of the line, however in the mark scheme they simplified the vectors to -2,3,1 for some reason and i don't understand why.

mark scheme here
http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf
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ciberyad
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Vectors which are parallel represent the same direction vector.

Two vectors \textbf{u} and \textbf{v} are parallel if and only if there is a non-zero scalar \lambda for which \textbf u=\lambda\textbf v.

In your case, the vectors \textbf{u}=\begin{pmatrix}-10\\15\\-5\end{pmatrix} and \textbf v=\begin{pmatrix}-2\\3\\-1\end{pmatrix} are parallel since \textbf u=5\textbf v.
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