Embibe Experts Solutions for Chapter: Plane, Exercise 1: MHT-CET 2017

A plane $E_1$ makes intercepts $1,-3,4$ on the co-ordinate axes. The equation of a plane parallel to plane $E_1$ and passing through $(2,6,-8)$ is

The equation of a plane containing the point $\left(1,-1,1\right)$ and parallel to the plane $2x+3y-4z=17$ is

If the foot of the perpendicular drawn from the point $(0,0,0)$ to the plane is $(4,-2,-5)$ then the equation of the plane is …..

If lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and  $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z-0}{1}$ intersect, then the value of $k$ is

The distance of the point $(3,4,5)$ from the point of intersection of the line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}$ and plane $x+y+z=2$ is

Equations of planes parallel to the plane $x-2y+2z+4=0$ which are at a distance of one unit from the point $\left(\mathrm{1,2},3\right)$ are …..

If $O\equiv \left(0,0,0\right), P\equiv (1,\sqrt{2},1),$ then the acute angles made by the line $OP$ with $XOY$, $YOZ, ZOX$ planes are, respectively

The angle between the line $\frac{x-1}{2}=\frac{y+3}{1}=\frac{z+7}{2}$ and the plane $\overrightarrow{r}·\left(6\hat{\mathrm{ı}}-2\hat{\mathrm{ȷ}}-3\hat{\mathrm{k}}\right)=5$ is