3D Geometry

Showing 31-35 of 461 questions.

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JEE Main 2023 (Online) 6th April Evening ShiftQuestion 31

A plane $P$ contains the line of intersection of the plane $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6$ and $\vec{r}\cdot\left(2\hat{i}+3\hat{j}+4\hat{k}\right)=-5$. If $P$ passes through the point $(0,2,-2)$, then the square of distance of the point $(12,12,18)$ from the plane $P$ is

3D Geometry

$155$$310$$620$$1240$

JEE Main 2021 (Online) 3rd August Morning ShiftQuestion 32

The distance of the origin from the point of intersection of the line, $\frac{x}{2}=\frac{y+1}{3}=\frac{z-1}{-1}$ and the plane, $2x+y+6z+1=0$ is

3D Geometry

$4\sqrt{6}$$2\sqrt{3}$$\sqrt{544}$$\sqrt{554}$

JEE Main 2021 (Online) 26th February Evening ShiftQuestion 33

Let $L$ be a line obtained from the intersection of two planes $x+2y+z=6$ and $y+2z=4$. If point $P(\alpha,\beta,\gamma)$ is the foot of perpendicular from $(3,2,1)$ on $L$, then the value of $21(\alpha+\beta+\gamma)$ equals :

3D Geometry

$68$$102$$136$$142$

JEE Main 2021 (Online) 26th February Evening ShiftQuestion 34

If the mirror image of the point $(1,3,5)$ with respect to the plane $4x-5y+2z=8$ is $(\alpha,\beta,\gamma)$, then $5(\alpha+\beta+\gamma)$ equals :

3D Geometry

$39$$41$$43$$47$

JEE Main 2021 (Online) 26th August Evening ShiftQuestion 35

Let $P$ be the plane passing through the point $(1,2,3)$ and the line of intersection of the planes $\vec{r}\cdot\left(\hat{i}+\hat{j}+4\hat{k}\right)=16$ and $\vec{r}\cdot\left(-\hat{i}+\hat{j}+\hat{k}\right)=6$. Then which of the following points does NOT lie on $P$ ?

3D Geometry

$(-8,8,6)$$(6,-6,2)$$(4,2,2)$$(3,3,2)$