If the lines given by frac{x - 1}{2 lambda} = | vedclass

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(D) The direction ratios of the first line $\frac{x - 1}{2 \lambda} = \frac{y - 1}{-5} = \frac{z - 1}{2}$ are $(2 \lambda, -5, 2)$.The direction ratio

Vedclass · Accepted Answer

$\frac{-5}{2}$

Vedclass · Answer

(D) The direction ratios of the first line $\frac{x - 1}{2 \lambda} = \frac{y - 1}{-5} = \frac{z - 1}{2}$ are $(2 \lambda, -5, 2)$.The direction ratios of the second line $\frac{x + 2}{\lambda} = \frac{y + 3}{\lambda} = \frac{z + 5}{1}$ are $(\lambda, \lambda, 1)$.Since the two lines are parallel,their direction ratios must be proportional:$\frac{2 \lambda}{\lambda} = \frac{-5}{\lambda} = \frac{2}{1}$.From the ratio $\frac{-5}{\lambda} = \frac{2}{1}$,we get $2 \lambda = -5$,which implies $\lambda = \frac{-5}{2}$.Checking the first ratio: $\frac{2 \lambda}{\lambda} = 2$,which is consistent with the third ratio $\frac{2}{1} = 2$ for $\lambda 
eq 0$.

If the lines given by $\frac{x - 1}{2 \lambda} = \frac{y - 1}{-5} = \frac{z - 1}{2}$ and $\frac{x + 2}{\lambda} = \frac{y + 3}{\lambda} = \frac{z + 5}{1}$ are parallel,then the value of $\lambda$ is

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