3D Geometry

Showing 96-100 of 461 questions.

Page 20 of 93

JEE Main 2024 (Online) 6th April Morning ShiftQuestion 96

If $A(3,1,-1)$, $B\left(\frac{5}{3},\frac{7}{3},\frac{1}{3}\right)$, $C(2,2,1)$ and $D\left(\frac{10}{3},\frac{2}{3},\frac{-1}{3}\right)$ are the vertices of a quadrilateral $ABCD$, then its area is

3D Geometry

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

JEE Main 2025 (Online) 4th April Evening ShiftQuestion 97

Let $A$ be the point of intersection of the lines $L_1:\frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1}$ and $L_2:\frac{x-1}{3}=\frac{y+3}{4}=\frac{z+7}{5}$. Let $B$ and $C$ be the points on the lines $L_1$ and $L_2$ respectively such that $AB=AC=\sqrt{15}$. Then the square of the area of the triangle $ABC$ is :

3D Geometry

$54$$60$$63$$57$

JEE Main 2024 (Online) 9th April Evening ShiftQuestion 98

Consider the line $L$ passing through the points $(1,2,3)$ and $(2,3,5)$. The distance of the point $\left(\frac{11}{3},\frac{11}{3},\frac{19}{3}\right)$ from the line $L$ along the line $\frac{3x-11}{2}=\frac{3y-11}{1}=\frac{3z-19}{2}$ is equal to

3D Geometry

$6$$5$$4$$3$

JEE Main 2023 (Online) 15th April Morning ShiftQuestion 99

Let $S$ be the set of all values of $\lambda$, for which the shortest distance between the lines $\frac{x-\lambda}{0}=\frac{y-3}{4}=\frac{z+6}{1}$ and $\frac{x+\lambda}{3}=\frac{y}{-4}=\frac{z-6}{0}$ is $13$. Then $8\left|\sum_{\lambda\in S}\lambda\right|$ is equal to

3D Geometry

$302$$304$$306$$308$

JEE Main 2025 (Online) 7th April Evening ShiftQuestion 100

If the equation of the line passing through the point $\left(0,-\frac{1}{2},0\right)$ and perpendicular to the lines $\vec{r}=\lambda\left(\hat{i}+a\hat{j}+b\hat{k}\right)$ and $\vec{r}=\left(\hat{i}-\hat{j}-6\hat{k}\right)+\mu\left(-b\hat{i}+a\hat{j}+5\hat{k}\right)$ is $\frac{x-1}{-2}=\frac{y+4}{d}=\frac{z-c}{-4}$, then $a+b+c+d$ is equal to :

3D Geometry

$10$$12$$13$$14$