3D Geometry

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JEE Main 2022 (Online) 29th June Morning ShiftQuestion 136

If the mirror image of the point $(2,4,7)$ in the plane $3x-y+4z=2$ is $(a,b,c)$, then $2a+b+2c$ is equal to :

3D Geometry

$54$$50$$-6$$-42$

JEE Main 2020 (Online) 3rd September Evening ShiftQuestion 137

The plane which bisects the line joining the points $(4,-2,3)$ and $(2,4,-1)$ at right angles also passes through the point :

3D Geometry

$(4,0,1)$$(4,0,-1)$$(0,-1,1)$$(0,1,-1)$

JEE Main 2022 (Online) 29th July Evening ShiftQuestion 138

If $(2,3,9)$, $(5,2,1)$, $(1,\lambda,8)$ and $(\lambda,2,3)$ are coplanar, then the product of all possible values of $\lambda$ is :

3D Geometry

$\frac{21}{2}$$\frac{59}{8}$$\frac{57}{8}$$\frac{95}{8}$

JEE Main 2020 (Online) 4th September Evening ShiftQuestion 139

The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac x2=\frac y3=\frac z{-6}$ is :

3D Geometry

$\frac17$$1$$7$$\frac75$

JEE Main 2022 (Online) 30th July Evening ShiftQuestion 140

Let $ax+by+cz+3=0$ be the plane which bisects the acute angle between the planes $2x-y-2z+3=0$ and $3x-2y+6z+8=0$. Then $a+b+c$ is equal to

3D Geometry

$-31$$28$$\frac{14}{15}$$-28$