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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

The shortest distance between the lines $\frac{x - 3}{2} = \frac{y + 15}{-7} = \frac{z - 9}{5}$ and $\frac{x + 1}{2} = \frac{y - 1}{1} = \frac{z - 9}{-3}$ is

The distance of the point $(-2, 4, -5)$ from the line $\frac{x+3}{3} = \frac{y-4}{5} = \frac{z+8}{6}$ is

The equation of the $x$-axis is:

The foot of the perpendicular from $(0,2,3)$ to the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ is

Let $\lambda$ be an integer. If the shortest distance between the lines $x - \lambda = 2y - 1 = -2z$ and $x = y + 2\lambda = z - \lambda$ is $\frac{\sqrt{7}}{2\sqrt{2}}$,then the value of $|\lambda|$ is ...... .

Vedclass Test Series

Exam Paper Generator

Online Exam Module