JEE Main 2025 (Online) 2nd April Evening ShiftQuestion 66
If the image of the point $P(1,0,3)$ in the line joining the points $A(4,7,1)$ and $B(3,5,3)$ is $Q(\alpha,\beta,\gamma)$, then $\alpha+\beta+\gamma$ is equal to :
3D Geometry
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3D Geometry
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JEE Main 2025 (Online) 8th April Evening ShiftQuestion 67
Let the values of $\lambda$ for which the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-\lambda}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{6}}$ be $\lambda_1$ and $\lambda_2$. Then the radius of the circle passing through the points $(0,0)$, $(\lambda_1,\lambda_2)$ and $(\lambda_2,\lambda_1)$ is
3D Geometry
JEE Main 2024 (Online) 1st February Morning ShiftQuestion 68
If the shortest distance between the lines $\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and $\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1}$ is $1$, then the sum of all possible values of $\lambda$ is :
3D Geometry
JEE Main 2025 (Online) 2nd April Morning ShiftQuestion 69
Let the vertices $Q$ and $R$ of the triangle $PQR$ lie on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$, $QR=5$ and the coordinates of the point $P$ be $(0,2,3)$. If the area of the triangle $PQR$ is $\frac{m}{n}$ then :
3D Geometry
JEE Main 2024 (Online) 9th April Morning ShiftQuestion 70
Let the line $L$ intersect the lines $x-2=-y=z-1$, $2(x+1)=2(y-1)=z+1$ and be parallel to the line $\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}$. Then which of the following points lies on $L$?
3D Geometry