Direction ratios of a vector parallel to line \(\frac{x-1}{2}=-y=\frac{2 z+1}{6}\) are :

Let \(\frac{x-1}{2}=-y=\frac{2 z+1}{6}=\lambda\)

\(x=1+2 \lambda \Rightarrow \frac{d x}{d \lambda}=2\)

\(-y=\lambda \Rightarrow y=-\lambda\)

\(\Rightarrow \frac{d y}{d \lambda}=-1\)

\(\frac{2 z+1}{6}=\lambda \Rightarrow 2 z=6 \lambda-1\)

\(\Rightarrow z=3 \lambda-\frac{1}{2} \Rightarrow \frac{d z}{d \lambda}=3\)