3D Geometry

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JEE Main 2019 (Online) 10th April Evening ShiftQuestion 286

If the plane $2x-y+2z+3=0$ has the distances $\frac13$ and $\frac23$ units from the planes $4x-2y+4z+\lambda=0$ and $2x-y+2z+\mu=0$, respectively, then the maximum value of $\lambda+\mu$ is equal to :

3D Geometry

$9$$15$$13$$5$

JEE Main 2015 (Online) 11th AprilQuestion 287

A plane containing the point $(3,2,0)$ and the line $\frac{x-1}{1}=\frac{y-2}{5}=\frac{z-3}{4}$ also contains the point

3D Geometry

$(0,7,-10)$$(0,7,10)$$(0,3,1)$$(0,-3,1)$

JEE Main 2018 (Offline)Question 288

The length of the projection of the line segment joining the points $(5,-1,4)$ and $(4,-1,3)$ on the plane $x+y+z=7$ is

3D Geometry

$\sqrt{\frac23}$$\frac2{\sqrt3}$$\frac23$$\frac13$

JEE Main 2018 (Online) 15th April Morning ShiftQuestion 289

An angle between the plane, $x+y+z=5$ and the line of intersection of the planes, $3x+4y+z-1=0$ and $5x+8y+2z+14=0$, is

3D Geometry

$\cos^{-1}\left(\frac3{\sqrt{17}}\right)$$\cos^{-1}\left(\sqrt{\frac3{17}}\right)$$\sin^{-1}\left(\frac3{\sqrt{17}}\right)$$\sin^{-1}\left(\sqrt{\frac3{17}}\right)$

JEE Main 2016 (Offline)Question 290

The distance of the point $(1,-5,9)$ from the plane $x-y+z=5$ measured along the line $x=y=z$ is

3D Geometry

$\frac{10}{\sqrt3}$$\frac{20}{3}$$3\sqrt{10}$$10\sqrt3$