Embibe Experts Solutions for Chapter: Line in 3D, Exercise 1: MHT-CET 2020 (13-Oct Shift 1)

The equation of the line passing through the point $(2,3,-4)$ and perpendicular to the $XOZ$ plane is $\left(\lambda \in R\right)$

If the Cartesian equation of the line is $x-1=2y+3=3-z,$ then its vector equation is

The parametric equations of the line passing through $A\left(3, 4, -7\right), B\left(1,-1, 6\right)$ are $\left(\lambda \in R\right)$

If line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\lambda }{2}=\frac{z}{1}$ intersect each other, then $\lambda =.\dots .$

The equation of line equally inclined to co-ordinate axes and passing through $\left(-3,2,-5\right)$ is

The lines $\frac{x-1}{2}=\frac{y+1}{2}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-6}{2}=\frac{z}{1}$ intersect each other at point

The shortest distance between the lines $\overrightarrow{r}=(1-t)\hat{i}+(t-2)\hat{j}+(3-2t)\hat{k}$ and $\overrightarrow{r}=(p+1)\hat{i}+(2p-1)\hat{ȷ}+(2p+1)\hat{k}$ is