Embibe Experts Solutions for Chapter: Three Dimensional Geometry, Exercise 2: EXERCISE-2

The lines $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{\lambda }$ and $\frac{x}{1}=\frac{y}{2}=\frac{z+1}{-1}$ are-

The equation of a plane bisecting the angle between the plane $2x-y+2z+3=0$ and $3x-2y+6z+8=0$ is-

If $l_1, m_1, n_1$ and $l_2, m_2, n_2$ are direction cosines of the two lines inclined to each other at an angle $\theta$, then the direction cosines of the bisector of the angle between these lines are-

Points that lie on the lines bisecting the angle between the lines $\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-6}{6}$ and $\frac{x-2}{3}=\frac{y-3}{6}=\frac{z-6}{2}$ are-

Consider the plane $\overrightarrow{r}\cdot {\overrightarrow{n}}_1={\overrightarrow{d}}_1$ and $\overrightarrow{r}\cdot {\overrightarrow{n}}_2={\overrightarrow{d}}_2$, then which of the following true

The equation of the plane which contains lines $\overrightarrow{r}=\widehat{i}+2\widehat{j}-\widehat{k}+\lambda \left(\widehat{i}+2\widehat{j}-\widehat{k}\right)$ and $\overrightarrow{r}=\widehat{i}+2\widehat{j}-\widehat{k}+\mu \left(\widehat{i}+\widehat{j}+3\widehat{k}\right)$ must be

The plane containing the lines $\overrightarrow{r}=\overrightarrow{a}+t\overrightarrow{a}\text{'}$ and $\overrightarrow{r}=\overrightarrow{a}\text{'}+s\overrightarrow{a}$-

The points $A\left(5, -1, 1\right), B\left(7, -4, 7\right), C\left(1, -6, 10\right)$ and $D\left(-1, -3, 4\right)$ are the vertices of a