Q49 / 155 · WBJEE 2022 · Mathematics

The equation of the plane through the intersection of the planes $x+y+z=1$ and $2 x+3 y-z+4$ and parallel to the $x$-axis is

A
$y+3 z+6=0$
B
$y+3 z-6=0$
Correct answer
C
$y-3 z+6=0$
D
$y-3 z-6=0$

Solution

$\quad(2 x+3 y-z+4)+\lambda(x + y+z-1)=0$ $\overrightarrow{\mathrm{n}}=(2+\lambda) \hat{\mathrm{i}}+(3+\lambda) \hat{\mathrm{j}}+(-1+\lambda) \hat{\mathrm{k}}$ $\overrightarrow{\mathrm{n}} \cdot \overrightarrow{\mathrm{i}}=0 \Rightarrow \lambda=-2$ $\Rightarrow \mathrm{y}-3 z+6=0$

Hence, the correct answer is option: 'C'.

Relevant Questions

Intercepts of the plane on the coordinate axes respectively are2026Plane in Space
The plane is rotated through about its line of intersection with the plane . The equation of the plane in new position is2024Plane in Space
If from a point , perpendiculars and are drawn to and planes respectively, then the equation of the plane is2021Plane in Space
The plane is rotated about its line of intersection with the plane through an angle . The equation changes to2021Plane in Space
The equation of the plane, which bisects the line joining the points (1,2,3) and (3,4,5) at right angles is2019Plane in Space
The equation of the plane through (1,2,-3) and (2,-2,1) and parallel to -axis is2017Plane in Space