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3D Geometry

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JEE Main 2023 (Online) 30th January Morning ShiftQuestion 351

If $\lambda_1<\lambda_2$ are two values of $\lambda$ such that the angle between the planes $P_1:\vec r\cdot\left(3\hat i-5\hat j+\hat k\right)=7$ and $P_2:\vec r\cdot\left(\lambda\hat i+\hat j-3\hat k\right)=9$ is $\sin^{-1}\left(\frac{2\sqrt6}{5}\right)$, then the square of the length of perpendicular from the point $\left(38\lambda_1,10\lambda_2,2\right)$ to the plane $P_1$ is ______.

3D Geometry

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IIT-JEE 2004 ScreeningQuestion 352

If the lines $\dfrac{x-1}{2}=\dfrac{y+1}{3}=\dfrac{z-1}{4}$ and $\dfrac{x-3}{1}=\dfrac{y-k}{2}=\dfrac{z}{1}$ intersect, then the value of $k$ is

3D Geometry

$3/2$$9/2$$-2/9$$-3/2$

IIT-JEE 2004Question 353

Find the equation of the plane passing through $(1,1,1)$ and parallel to the lines $L_1,L_2$ having direction ratios $(1,0,-1)$, $(1,-1,0)$. Find the volume of the tetrahedron formed by the origin and the points where this plane intersects the coordinate axes.

3D Geometry

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IIT-JEE 2005Question 354

Find the equation of the plane containing the lines $2x-y+z-3=0$, $3x+y+z=5$ and at a distance of $\dfrac{1}{\sqrt6}$ from the point $(2,1,-1)$.

3D Geometry

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IIT-JEE 2003 ScreeningQuestion 355

The value of $k$ such that $\dfrac{x-4}{1}=\dfrac{y-2}{1}=\dfrac{z-k}{2}$ lies in the plane $2x-4y+z=7$, is

3D Geometry

$7$$-7$no real value$4$