3D Geometry

Showing 406-410 of 461 questions.

Page 82 of 93

JEE Main 2025 (Online) 28th January Morning ShiftQuestion 406

Let $A(x,y,z)$ be a point in $xy$-plane, which is equidistant from three points $(0,3,2)$, $(2,0,3)$ and $(0,0,1)$. Let $B=(1,4,-1)$ and $C=(2,0,-2)$. Then among the statements $(S1)$ : $\triangle ABC$ is an isosceles right angled triangle, and $(S2)$ : the area of $\triangle ABC$ is $\frac{9\sqrt{2}}{2}$,

3D Geometry

both are trueboth are falseonly $(S1)$ is trueonly $(S2)$ is true

JEE Main 2025 (Online) 23rd January Evening ShiftQuestion 407

The distance of the line $\frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{4}$ from the point $(1,4,0)$ along the line $\frac{x}{1}=\frac{y-2}{2}=\frac{z+3}{3}$ is :

3D Geometry

$\sqrt{14}$$\sqrt{15}$$\sqrt{13}$$\sqrt{17}$

Comprehension · Questions 408–410

Read the passage given below and answer the questions that follow.

Consider the lines $$L_1:\frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}$$ $$L_2:\frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3}$$

JEE Advanced 2008 Paper 2Question 408

The unit vector perpendicular to both $L_1$ and $L_2$ is

3D Geometry

$\frac{-\hat{i}+7\hat{j}+7\hat{k}}{\sqrt{99}}$$\frac{-\hat{i}-7\hat{j}+5\hat{k}}{5\sqrt{3}}$$\frac{-\hat{i}+7\hat{j}+5\hat{k}}{5\sqrt{3}}$$\frac{7\hat{i}-7\hat{j}-\hat{k}}{\sqrt{99}}$

JEE Advanced 2008 Paper 2Question 409

The shortest distance between $L_1$ and $L_2$ is

3D Geometry

$0$$\frac{17}{\sqrt{3}}$$\frac{41}{5\sqrt{3}}$$\frac{17}{5\sqrt{3}}$

JEE Advanced 2008 Paper 2Question 410

The distance of the point $(1,1,1)$ from the plane passing through the point $(-1,-2,-1)$ and whose normal is perpendicular to both the lines $L_1$ and $L_2$ is

3D Geometry

$\frac{2}{\sqrt{75}}$$\frac{7}{\sqrt{75}}$$\frac{13}{\sqrt{75}}$$\frac{23}{\sqrt{75}}$