JEE Mathematics / Practice

3D Geometry

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JEE Main 2021 (Online) 18th March Evening ShiftQuestion 156

Let $P$ be a plane containing the line $\frac{x-1}{3}=\frac{y+6}{4}=\frac{z+5}{2}$ and parallel to the line $\frac{x-3}{4}=\frac{y-2}{-3}=\frac{z+5}{7}$. If the point $(1,-1,\alpha)$ lies on the plane $P$, then the value of $|5\alpha|$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2026 (Online) 6th April Evening ShiftQuestion 157

Let the image of the point $P(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point $R$ and the image of the point $Q\left(0,\frac{-1}{2},0\right)$ in the line $\frac{x-1}{-1}=\frac{y+9}{4}=\frac{z+1}{1}$ be the point $S$. Then the square of the area of the parallelogram $PQRS$ is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2021 (Online) 24th February Evening ShiftQuestion 158

Let $\lambda$ be an integer. If the shortest distance between the lines $x-\lambda=2y-1=-2z$ and $x=y+2\lambda=z-\lambda$ is $\frac{\sqrt{7}}{2\sqrt{2}}$, then the value of $|\lambda|$ is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2021 (Online) 31st August Morning ShiftQuestion 159

The square of the distance of the point of intersection of the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+1}{6}$ and the plane $2x-y+z=6$ from the point $(-1,-1,2)$ is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2022 (Online) 30th June Morning ShiftQuestion 160

Consider a triangle $ABC$ whose vertices are $A(0,\alpha,\alpha)$, $B(\alpha,0,\alpha)$ and $C(\alpha,\alpha,0)$, $\alpha>0$. Let $D$ be a point moving on the line $x+z-3=0=y$ and $G$ be the centroid of $\triangle ABC$. If the minimum length of $GD$ is $\sqrt{\frac{57}{2}}$, then $\alpha$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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