JEE Mathematics / Practice

3D Geometry

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JEE Main 2022 (Online) 29th June Morning ShiftQuestion 171

Let $d$ be the distance between the foot of perpendiculars of the points $P(1,2,-1)$ and $Q(2,-1,3)$ on the plane $-x+y+z=1$. Then $d^{2}$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2024 (Online) 6th April Morning ShiftQuestion 172

Let $P$ be the point $(10,-2,-1)$ and $Q$ be the foot of the perpendicular drawn from the point $R(1,7,6)$ on the line passing through the points $(2,-5,11)$ and $(-6,7,-5)$. Then the length of the line segment $PQ$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2021 (Online) 26th August Evening ShiftQuestion 173

Let $Q$ be the foot of the perpendicular from the point $P(7,-2,13)$ on the plane containing the lines $\frac{x+1}{6}=\frac{y-1}{7}=\frac{z-3}{8}$ and $\frac{x-1}{3}=\frac{y-2}{5}=\frac{z-3}{7}$. Then $(PQ)^{2}$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2020 (Online) 9th January Evening ShiftQuestion 174

If the distance between the plane, $23x-10y-2z+48=0$ and the plane containing the lines $\frac{x+1}2=\frac{y-3}4=\frac{z+1}3$ and $\frac{x+3}2=\frac{y+2}6=\frac{z-1}\lambda$ ($\lambda\in\mathbf{R}$) is equal to $\frac k{\sqrt{633}}$, then $k$ is equal to ________.

3D Geometry

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JEE Main 2024 (Online) 29th January Morning ShiftQuestion 175

A line with direction ratios $2,1,2$ meets the lines $x=y+2=z$ and $x+2=2y=2z$ respectively at the points $P$ and $Q$. If the length of the perpendicular from the point $(1,2,12)$ to the line $PQ$ is $l$, then $l^{2}$ is $\_\_\_\_\_\_$ .

3D Geometry

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