3D Geometry

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JEE Main 2023 (Online) 13th April Evening ShiftQuestion 61

The plane, passing through the points $(0,-1,2)$ and $(-1,2,1)$ and parallel to the line passing through $(5,1,-7)$ and $(1,-1,-1)$, also passes through the point

3D Geometry

$(1,-2,1)$$(-2,5,0)$$(2,0,1)$$(0,5,-2)$

JEE Main 2023 (Online) 13th April Morning ShiftQuestion 62

Let the equation of plane passing through the line of intersection of the planes $x+2y+az=2$ and $x-y+z=3$ be $5x-11y+bz=6a-1$. For $c\in\mathbb{Z}$, if the distance of this plane from the point $(a,-c,c)$ is $\frac{2}{\sqrt{a}}$, then $\frac{a+b}{c}$ is equal to

3D Geometry

$-4$$-2$$2$$4$

JEE Main 2024 (Online) 31st January Evening ShiftQuestion 63

Let $(\alpha,\beta,\gamma)$ be the mirror image of the point $(2,3,5)$ in the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$. Then, $2\alpha+3\beta+4\gamma$ is equal to

3D Geometry

$31$$32$$33$$34$

JEE Main 2025 (Online) 7th April Morning ShiftQuestion 64

If the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x}{1}=\frac{y}{\alpha}=\frac{z-5}{1}$ is $\frac{5}{\sqrt{6}}$, then the sum of all possible values of $\alpha$ is

3D Geometry

$3$$-3$$\frac{3}{2}$$-\frac{3}{2}$

JEE Main 2024 (Online) 8th April Evening ShiftQuestion 65

If the shortest distance between the lines $\frac{x-\lambda}{2}=\frac{y-4}{3}=\frac{z-3}{4}$ and $\frac{x-2}{4}=\frac{y-4}{6}=\frac{z-7}{8}$ is $\frac{13}{\sqrt{29}}$, then a value of $\lambda$ is :

3D Geometry

$-1$$\frac{13}{25}$$1$$-\frac{13}{25}$