JEE Mathematics / Practice

3D Geometry

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JEE Main 2024 (Online) 8th April Evening ShiftQuestion 161

Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(1,6,4)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$. Then $2\alpha+\beta+\gamma$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2025 (Online) 8th April Evening ShiftQuestion 162

Let the area of the triangle formed by the lines $x+2=y-1=z$ and $\frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}$ and $\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}$ be $A$. Then $A^{2}$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2021 (Online) 4th August Morning ShiftQuestion 163

Maximum number of lines, through the origin which make equal angles with the three coordinate axes in $XYZ$-space, is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2024 (Online) 1st February Morning ShiftQuestion 164

Let the line of the shortest distance between the lines $L_1:\vec{r}=\left(\hat{i}+2\hat{j}+3\hat{k}\right)+\lambda\left(\hat{i}-\hat{j}+\hat{k}\right)$ and $L_2:\vec{r}=\left(4\hat{i}+5\hat{j}+6\hat{k}\right)+\mu\left(\hat{i}+\hat{j}-\hat{k}\right)$ intersect $L_1$ and $L_2$ at $P$ and $Q$ respectively. If $(\alpha,\beta,\gamma)$ is the mid point of the line segment $PQ$, then $2(\alpha+\beta+\gamma)$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2022 (Online) 26th July Morning ShiftQuestion 165

Let $Q$ and $R$ be two points on the line $\frac{x+1}{2}=\frac{y+2}{3}=\frac{z-1}{2}$ at a distance $\sqrt{26}$ from the point $P(4,2,7)$. Then the square of the area of the triangle $PQR$ is ________.

3D Geometry

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