3D Geometry

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JEE Main 2018 (Online) 16th AprilQuestion 296

If the angle between the lines $\frac x2=\frac y2=\frac z1$ and $\frac{5-x}{-2}=\frac{7y-14}{P}=\frac{z-3}{4}$ is $\cos^{-1}\left(\frac23\right)$, then $P$ is equal to

3D Geometry

$\frac27$$\frac72$$-\frac47$$-\frac74$

JEE Main 2019 (Online) 9th January Morning ShiftQuestion 297

The equation of the line passing through $(-4,3,1)$, parallel to the plane $x+2y-z-5=0$ and intersecting the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z-2}{-1}$ is

3D Geometry

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

JEE Main 2019 (Online) 12th January Morning ShiftQuestion 298

The perpendicular distance from the origin to the plane containing the two lines $\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}$ and $\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}$, is

3D Geometry

$11\sqrt6$$\frac{11}{\sqrt6}$$11$$6\sqrt{11}$

JEE Main 2016 (Online) 9th AprilQuestion 299

The distance of the point $(1,-2,4)$ from the plane passing through the point $(1,2,2)$ and perpendicular to the planes $x-y+2z=3$ and $2x-2y+z+12=0$, is :

3D Geometry

$2$$\sqrt2$$2\sqrt2$$\frac{1}{\sqrt2}$

JEE Main 2018 (Online) 15th April Evening ShiftQuestion 300

A plane bisects the line segment joining the points $(1,2,3)$ and $(-3,4,5)$ at right angles. Then this plane also passes through the point.

3D Geometry

$(-3,2,1)$$(3,2,1)$$(1,2,-3)$$(-1,2,3)$