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Since the ropes are parallel, the vectors representing them must be proportional. Therefore, we can write:
\[ \frac{3}{2} = \frac{15}{10} = \frac{6}{\lambda} \]From the first two ratios, we have \(\frac{3}{2} = \frac{3}{2}\), which confirms that the vectors are indeed parallel.
Now, we can use the first and third ratios to solve for \(\lambda\):
\[ \frac{3}{2} = \frac{6}{\lambda} \]Cross-multiplying, we get:
\[ 3\lambda = 12 \]Dividing both sides by 3, we find:
\[ \lambda = 4 \]Correct Answer: 4