3D Geometry

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JEE Main 2019 (Online) 9th April Morning ShiftQuestion 256

If the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4}$ meets the plane $x+2y+3z=15$ at a point $P$, then the distance of $P$ from the origin is

3D Geometry

$2\sqrt5$$\frac92$$\frac{\sqrt5}{2}$$\frac72$

JEE Main 2019 (Online) 10th January Evening ShiftQuestion 257

On which of the following lines lies the point of intersection of the line $\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}$ and the plane $x+y+z=2$?

3D Geometry

$\frac{x-4}{1}=\frac{y-5}{1}=\frac{z-5}{-1}$$\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+4}{-5}$$\frac{x-2}{2}=\frac{y-3}{2}=\frac{z+3}{3}$$\frac{x+3}{3}=\frac{4-y}{3}=\frac{z+1}{-2}$

JEE Main 2019 (Online) 9th April Morning ShiftQuestion 258

A plane passing through the points $(0,-1,0)$ and $(0,0,1)$ and making an angle $\frac\pi4$ with the plane $y-z+5=0$, also passes through the point

3D Geometry

$\left(\sqrt2,-1,4\right)$$\left(\sqrt2,1,4\right)$$\left(-\sqrt2,-1,-4\right)$$\left(-\sqrt2,1,-4\right)$

JEE Main 2019 (Online) 10th January Evening ShiftQuestion 259

The plane which bisects the line segment joining the points $(-3,-3,4)$ and $(3,7,6)$ at right angles, passes through which one of the following points?

3D Geometry

$(2,1,3)$$(4,1,-2)$$(4,-1,7)$$(-2,3,5)$

JEE Main 2023 (Online) 24th January Morning ShiftQuestion 260

The distance of the point $(7,-3,-4)$ from the plane containing the points $(2,-3,1)$, $(-1,1,-2)$ and $(3,-4,2)$ is equal to:

3D Geometry

$4$$5$$5\sqrt2$$4\sqrt2$