3D Geometry

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JEE Main 2023 (Online) 25th January Morning ShiftQuestion 301

The distance of the point $P(4,6,-2)$ from the line passing through the point $(-3,2,3)$ and parallel to a line with direction ratios $3,3,-1$ is equal to :

3D Geometry

$3$$\sqrt6$$2\sqrt3$$\sqrt{14}$

JEE Main 2023 (Online) 25th January Evening ShiftQuestion 302

The foot of perpendicular of the point $(2,0,5)$ on the line $\frac{x+1}{2}=\frac{y-1}{5}=\frac{z+1}{-1}$ is $(\alpha,\beta,\gamma)$. Then, which of the following is NOT correct?

3D Geometry

$\frac{\alpha\beta}{\gamma}=\frac{4}{15}$$\frac\alpha\beta=-8$$\frac\beta\gamma=-5$$\frac\gamma\alpha=\frac58$

JEE Main 2023 (Online) 29th January Evening ShiftQuestion 303

If the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{1}$ and $\frac{x-a}{2}=\frac{y+2}{3}=\frac{z-3}{1}$ intersects at the point $P$, then the distance of the point $P$ from the plane $z=a$ is :

3D Geometry

$16$$28$$10$$22$

JEE Main 2023 (Online) 29th January Evening ShiftQuestion 304

Shortest distance between the lines $\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}$ and $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}$ is

3D Geometry

$2\sqrt3$$4\sqrt3$$3\sqrt3$$5\sqrt3$

JEE Main 2025 (Online) 24th January Morning ShiftQuestion 305

Let the line passing through the points $(-1,2,1)$ and parallel to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac z4$ intersect the line $\frac{x+2}{3}=\frac{y-3}{2}=\frac{z-4}{1}$ at the point $P$. Then the distance of $P$ from the point $Q(4,-5,1)$ is

3D Geometry

$5$$5\sqrt5$$5\sqrt6$$10$