Skip to main content
Yukti Vault

JEE Mathematics / Practice

3D Geometry

Chapter overview and full question list

Showing 151-155 of 461 questions.

JEE Main 2021 (Online) 17th March Evening ShiftQuestion 151
Let $P$ be an arbitrary point having sum of the squares of the distances from the planes $x+y+z=0$, $lx-nz=0$ and $x-2y+z=0$, equal to $9$. If the locus of the point $P$ is $x^{2}+y^{2}+z^{2}=9$, then the value of $l-n$ is equal to $\_\_\_\_\_\_$ .
3D Geometry
JEE Main 2020 (Online) 8th January Evening ShiftQuestion 152
The mirror image of the point $(1,2,3)$ in a plane is $\left(-\frac73,-\frac43,-\frac13\right)$. Which of the following points lies on this plane ?
3D Geometry
Options for question 152, choose one
JEE Main 2021 (Online) 16th March Evening ShiftQuestion 153
If the distance of the point $(1,-2,3)$ from the plane $x+2y-3z+10=0$ measured parallel to the line, $\frac{x-1}{3}=\frac{2-y}{m}=\frac{z+3}{1}$ is $\sqrt{\frac{7}{2}}$, then the value of $|m|$ is equal to $\_\_\_\_\_\_$ .
3D Geometry
JEE Main 2026 (Online) 8th April Evening ShiftQuestion 154
Let a line $L_1$ pass through the origin and be perpendicular to the lines $L_2:\vec{r}=(3+t)\hat{i}+(2t-1)\hat{j}+(2t+4)\hat{k}$ and $L_3:\vec{r}=(3+2s)\hat{i}+(3+2s)\hat{j}+(2+s)\hat{k}$, $t,s\in\mathbf{R}$. If $(a,b,c)$, $a\in\mathbf{Z}$, is the point on $L_3$ at a distance of $\sqrt{17}$ from the point of intersection of $L_1$ and $L_2$, then $(a+b+c)^{2}$ is equal to $\_\_\_\_\_\_$ .
3D Geometry
JEE Main 2021 (Online) 25th February Evening ShiftQuestion 155
A line '$l$' passing through origin is perpendicular to the lines $l_1:\vec{r}=(3+t)\hat{i}+(-1+2t)\hat{j}+(4+2t)\hat{k}$ $l_2:\vec{r}=(3+2s)\hat{i}+(3+2s)\hat{j}+(2+s)\hat{k}$ If the co-ordinates of the point in the first octant on '$l_2$' at a distance of $\sqrt{17}$ from the point of intersection of '$l$' and '$l_1$' are $(a,b,c)$, then $18(a+b+c)$ is equal to $\_\_\_\_\_\_$ .
3D Geometry