3D Geometry

Showing 6-10 of 461 questions.

Page 2 of 93

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

The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is :

3D Geometry

$\frac{5\sqrt{6}}{6}$$2\sqrt{5}$$3\sqrt{5}$$4\sqrt{5}$

JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 7

Let the point $A$ be the foot of perpendicular drawn from the point $P(a,b,0)$ on the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-\alpha}{3}$. If the midpoint of the line segment $PA$ is $\left(0,\frac{3}{4},\frac{-1}{4}\right)$, then the value of $a^{2}+b^{2}+\alpha^{2}$ is equal to :

3D Geometry

$1$$2$$6$$9$

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 8

Let the foot of perpendicular from the point $(\lambda,2,3)$ on the line $\frac{x-4}{1}=\frac{y-9}{2}=\frac{z-5}{1}$ be the point $(1,\mu,2)$. Then the distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}$ and $\frac{x-\lambda}{2}=\frac{y-\mu}{3}=\frac{z+5}{6}$ is equal to :

3D Geometry

$\frac{12}{7}$$\frac{\sqrt{145}}{7}$$\frac{\sqrt{146}}{7}$$\frac{\sqrt{143}}{7}$

JEE Main 2026 (Online) 4th April Evening ShiftQuestion 9

The shortest distance between the lines $\vec{r}=\left(\frac{1}{3}\hat{i}+2\hat{j}+\frac{8}{3}\hat{k}\right)+\lambda\left(2\hat{i}-5\hat{j}+6\hat{k}\right)$ and $\vec{r}=\left(-\frac{2}{3}\hat{i}-\frac{1}{3}\hat{k}\right)+\mu\left(\hat{j}-\hat{k}\right)$, $\lambda,\mu\in\mathbb{R}$, is:

3D Geometry

$\sqrt{5}$$3$$2\sqrt{3}$$\sqrt{15}$

JEE Main 2023 (Online) 10th April Morning ShiftQuestion 10

Let $P$ be the point of intersection of the line $\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}$ and the plane $x+y+z=2$. If the distance of the point $P$ from the plane $3x-4y+12z=32$ is $q$, then $q$ and $2q$ are the roots of the equation

3D Geometry

$x^{2}+18x+72=0$$x^{2}-18x-72=0$$x^{2}+18x-72=0$$x^{2}-18x+72=0$