Embibe Experts Solutions for Chapter: Three Dimensional Geometry, Exercise 1: AMU-AT (B.Tech.) 2017

If $A, B, C, D$ are the points $\left(2,3,-1\right),\left(3,5,-3\right),\left(1,2,3\right),\left(3,5,7\right)$ respectively, then the angle between $AB$ and $CD$ is

Which statement is true for the line $\frac{x-4}{8}=\frac{y-2}{2}=\frac{z-3}{3}$ and plane having intercepts $-4,2$ and $3$ of the following.

The image of the point $(1,-1,1)$ in the plane $x-2 y+3 z+1=0$ is

The length of perpendicular from the point $\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ to the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$ is

The angle between the line $x-2 y+z=0=x+2 y-2 z$ and the plane $5 x-2 y-z+17=0$ is

The distance of point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ with the plane $x-y+z=5$ from the point with position vector $\hat{\mathrm{i}}-2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ is

The shortest distance between the lines $\overrightarrow{r}=(4\hat{i}-\hat{j})+\lambda (\hat{i}+2\hat{j}-3\hat{k})$ and $\overrightarrow{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu (2\hat{i}+4\hat{j}-5\hat{k})$ is

Let $A$ and $B$ be two points with position vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ respectively and let $C$ be a point dividing $AB$ internally and the position vector of $C$ on $AB$ is $\overrightarrow{c}=\lambda \overrightarrow{a}+\mu \overrightarrow{b},$ then