JEE Main 2019 (Online) 12th January Evening ShiftQuestion 266
If an angle between the line $\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}$ and the plane $x-2y-kz=3$ is $\cos^{-1}\left(\frac{2\sqrt2}{3}\right)$, then a value of $k$ is
3D Geometry
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3D Geometry
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JEE Main 2023 (Online) 24th January Morning ShiftQuestion 267
The distance of the point $(-1,9,-16)$ from the plane $2x+3y-z=5$ measured parallel to the line $\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}$ is
3D Geometry
JEE Main 2019 (Online) 9th January Evening ShiftQuestion 268
If the lines $x=ay+b$, $z=cy+d$ and $x=a'z+b'$, $y=c'z+d'$ are perpendicular, then
3D Geometry
JEE Main 2019 (Online) 11th January Morning ShiftQuestion 269
The plane containing the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z-1}{3}$ and also containing its projection on the plane $2x+3y-z=5$, contains which one of the following points ?
3D Geometry
JEE Advanced 2023 Paper 1Question 270
Let $\ell_1$ and $\ell_2$ be the lines $\vec r_1=\lambda(\hat i+\hat j+\hat k)$ and $\vec r_2=(\hat j-\hat k)+\mu(\hat i+\hat k)$, respectively. Let $X$ be the set of all the planes $H$ that contain the line $\ell_1$. For a plane $H$, let $d(H)$ denote the smallest possible distance between the points of $\ell_2$ and $H$. Let $H_0$ be a plane in $X$ for which $d(H_0)$ is the maximum value of $d(H)$ as $H$ varies over all planes in $X$.
Match each entry in List-I to the correct entries in List-II.
List-I
(P) The value of $d(H_0)$ is
(Q) The distance of the point $(0,1,2)$ from $H_0$ is
(R) The distance of origin from $H_0$ is
(S) The distance of origin from the point of intersection of planes $y=z$, $x=1$ and $H_0$ is
List-II
(1) $\sqrt3$
(2) $\frac{1}{\sqrt3}$
(3) 0
(4) $\sqrt2$
(5) $\frac{1}{\sqrt2}$
The correct option is:
3D Geometry