JEE Mathematics / Practice

3D Geometry

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JEE Main 2024 (Online) 30th January Morning ShiftQuestion 206

If $d_1$ is the shortest distance between the lines $x+1=2y=-12z$, $x=y+2=6z-6$ and $d_2$ is the shortest distance between the lines $\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}$, $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}$, then the value of $\frac{32\sqrt{3}d_1}{d_2}$ is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2021 (Online) 4th August Morning ShiftQuestion 207

If the distance between the point $(a,-1,1)$ ($a>0$) and the plane passing through the points $(1,-2,1)$, $(3,1,0)$ and $(2,0,1)$ is $\frac{7}{\sqrt{6}}$, then the value of '$a$' is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2020 (Online) 4th September Morning ShiftQuestion 208

If the equation of a plane $P$, passing through the intersection of the planes, $x+4y-z+7=0$ and $3x+y+5z=8$ is $ax+by+6z=15$ for some $a,b\in\mathbf{R}$, then the distance of the point $(3,2,-1)$ from the plane $P$ is ________.

3D Geometry

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JEE Main 2026 (Online) 4th April Morning ShiftQuestion 209

The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line $\frac{x+5}{1}=\frac{y+5}{-1}=\frac{z}{2}$ is equal to :

3D Geometry

$3$$6$$8$$12$

JEE Main 2014 (Online) 11th AprilQuestion 210

Let $A(2,3,5)$, $B(-1,3,2)$ and $C(\lambda,5,\mu)$ be the vertices of a $\triangle ABC$. If the median through $A$ is equally inclined to the coordinate axes, then :

3D Geometry

$5\lambda-8\mu=0$$8\lambda-5\mu=0$$10\lambda-7\mu=0$$7\lambda-10\mu=0$