3D Geometry

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JEE Main 2022 (Online) 26th June Morning ShiftQuestion 86

Let the plane $2x+3y+z+20=0$ be rotated through a right angle about its line of intersection with the plane $x-3y+5z=8$. If the mirror image of the point $\left(2,-\frac{1}{2},2\right)$ in the rotated plane is $B(a,b,c)$, then :

3D Geometry

$\frac{a}{8}=\frac{b}{5}=\frac{c}{-4}$$\frac{a}{4}=\frac{b}{5}=\frac{c}{-2}$$\frac{a}{8}=\frac{b}{-5}=\frac{c}{4}$$\frac{a}{4}=\frac{b}{5}=\frac{c}{2}$

JEE Main 2024 (Online) 6th April Morning ShiftQuestion 87

The shortest distance between the lines $\frac{x-3}{2}=\frac{y+15}{-7}=\frac{z-9}{5}$ and $\frac{x+1}{2}=\frac{y-1}{1}=\frac{z-9}{-3}$ is

3D Geometry

$6\sqrt{3}$$5\sqrt{3}$$4\sqrt{3}$$8\sqrt{3}$

JEE Main 2025 (Online) 3rd April Evening ShiftQuestion 88

The distance of the point $(7,10,11)$ from the line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is

3D Geometry

$12$$14$$16$$18$

JEE Main 2024 (Online) 6th April Evening ShiftQuestion 89

Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(3,-3,1)$ in the line $\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1}$ and $R$ be the point $(2,5,-1)$. If the area of the triangle $PQR$ is $\lambda$ and $\lambda^{2}=14K$, then $K$ is equal to :

3D Geometry

$18$$36$$72$$81$

JEE Main 2024 (Online) 30th January Morning ShiftQuestion 90

Let $(\alpha,\beta,\gamma)$ be the foot of perpendicular from the point $(1,2,3)$ on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$. Then $19(\alpha+\beta+\gamma)$ is equal to :

3D Geometry

$99$$100$$101$$102$