Embibe Experts Solutions for Chapter: Plane, Exercise 1: Exercise 1

If the lines $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda }$ and $\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$ are coplanar, then ${\sin }^{-1}\left(\sin \lambda \right)+{\cos }^{-1}\left(\cos \lambda \right)=$

What is the distance of the point $(2,3,4)$ from the plane $3x-6y+2z+11=0?$

The equation of the plane passing through the line of intersection of the planes $x+y+z=1, 2x+3y+4z=7$, and perpendicular to the plane $x-5y+3z=5$ is given by

Consider the following statements:

I. Equation of plane parallel to $X$-axis is $x=0$.

II. Projection of $P\left(x,y,z\right)$ on the plane $YOZ$ is $(0,y,z)$.

Which of the above statement(s) is/are correct?

What is the distance between the planes $x-2y+z-1=0$ and $-3x+6y-3z+2=0?$

The plane through the intersection of planes $x+y+z=1$ and $2x+3y-z+4=0$ and parallel to $Y-$axis, also passes through the point

Let $L$ be a line obtained from the intersection of two planes $x+2y+z=6$ and $y+2z=4$. If point $P\left(\alpha ,\beta ,\gamma \right)$ is the foot of perpendicular from $\left(3,2,1\right)$ on $L$, then the value of $21\left(\alpha +\beta +\gamma \right)$ equals:

The vector equation of the plane passing through the intersection of the planes $\overrightarrow{r}·\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)=1$ and $\overrightarrow{r}·\left(\hat{\mathrm{i}}-2\hat{\mathrm{j}}\right)=-2,$ and the point $\left(1, 0, 2\right)$ is: