JEE Mathematics / Practice

3D Geometry

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JEE Main 2022 (Online) 24th June Morning ShiftQuestion 191

If the shortest distance between the lines $\vec{r}=\left(-\hat{i}+3\hat{k}\right)+\lambda\left(\hat{i}-a\hat{j}\right)$ and $\vec{r}=\left(-\hat{j}+2\hat{k}\right)+\mu\left(\hat{i}-\hat{j}+\hat{k}\right)$ is $\sqrt{\frac{2}{3}}$, then the integral value of $a$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2024 (Online) 31st January Morning ShiftQuestion 192

Let $Q$ and $R$ be the feet of perpendiculars from the point $P(a,a,a)$ on the lines $x=y,\ z=1$ and $x=-y,\ z=-1$ respectively. If $\angle QPR$ is a right angle, then $12a^{2}$ is equal to $\_\_\_\_\_\_$ .

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JEE Main 2021 (Online) 25th July Evening ShiftQuestion 193

If the lines $\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1}$ are co-planar, then the value of $k$ is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2024 (Online) 9th April Evening ShiftQuestion 194

The square of the distance of the image of the point $(6,1,5)$ in the line $\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$, from the origin is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2021 (Online) 27th August Evening ShiftQuestion 195

Let $S$ be the mirror image of the point $Q(1,3,4)$ with respect to the plane $2x-y+z+3=0$ and let $R(3,5,\gamma)$ be a point of this plane. Then the square of the length of the line segment $SR$ is $\_\_\_\_\_\_$ .

3D Geometry

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