3D Geometry

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JEE Main 2020 (Online) 6th September Evening ShiftQuestion 121

A plane $P$ meets the coordinate axes at $A$, $B$ and $C$ respectively. The centroid of $\Delta ABC$ is given to be $(1,1,2)$. Then the equation of the line through this centroid and perpendicular to the plane $P$ is :

3D Geometry

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

JEE Main 2022 (Online) 27th June Evening ShiftQuestion 122

The shortest distance between the lines $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1}$ and $\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}$, is

3D Geometry

$\frac{18}{\sqrt{5}}$$\frac{22}{3\sqrt{5}}$$\frac{46}{3\sqrt{5}}$$6\sqrt{3}$

JEE Main 2022 (Online) 27th June Morning ShiftQuestion 123

If two straight lines whose direction cosines are given by the relations $l+m-n=0$, $3l^{2}+m^{2}+cnl=0$ are parallel, then the positive value of $c$ is :

3D Geometry

$6$$4$$3$$2$

JEE Main 2022 (Online) 29th July Evening ShiftQuestion 124

Let $Q$ be the foot of perpendicular drawn from the point $P(1,2,3)$ to the plane $x+2y+z=14$. If $R$ is a point on the plane such that $\angle PRQ=60^\circ$, then the area of $\Delta PQR$ is equal to :

3D Geometry

$\frac{\sqrt3}{2}$$\sqrt3$$2\sqrt3$$3$

JEE Main 2022 (Online) 27th July Evening ShiftQuestion 125

If the length of the perpendicular drawn from the point $P(a,4,2)$, $a>0$ on the line $\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}$ is $2\sqrt6$ units and $Q(\alpha_1,\alpha_2,\alpha_3)$ is the image of the point $P$ in this line, then $a+\sum_{i=1}^{3}\alpha_i$ is equal to :

3D Geometry

$7$$8$$12$$14$