3D Geometry

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JEE Main 2020 (Online) 2nd September Evening ShiftQuestion 111

A plane passing through the point $(3,1,1)$ contains two lines whose direction ratios are $1,-2,2$ and $2,3,-1$ respectively. If this plane also passes through the point $(\alpha,-3,5)$, then $\alpha$ is equal to :

3D Geometry

$10$$-5$$5$$-10$

JEE Main 2022 (Online) 29th June Evening ShiftQuestion 112

Let $\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}$ lie on the plane $px-qy+z=5$, for some $p,q\in\mathbf{R}$. The shortest distance of the plane from the origin is:

3D Geometry

$\sqrt{\frac{3}{109}}$$\sqrt{\frac{5}{142}}$$\frac{5}{\sqrt{71}}$$\frac{1}{\sqrt{142}}$

JEE Main 2022 (Online) 28th July Evening ShiftQuestion 113

Let the lines $\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}$ be coplanar and $P$ be the plane containing these two lines. Then which of the following points does NOT lie on $P$?

3D Geometry

$(0,-2,-2)$$(-5,0,-1)$$(3,-1,0)$$(0,4,5)$

JEE Main 2020 (Online) 3rd September Morning ShiftQuestion 114

The foot of the perpendicular drawn from the point $(4,2,3)$ to the line joining the points $(1,-2,3)$ and $(1,1,0)$ lies on the plane :

3D Geometry

$x+2y-z=1$$x-2y+z=1$$x-y-2z=1$$2x+y-z=1$

JEE Main 2021 (Online) 17th March Morning ShiftQuestion 115

If the equation of the plane passing through the line of intersection of the planes $2x-7y+4z-3=0$, $3x-5y+4z+11=0$ and the point $(-2,1,3)$ is $ax+by+cz-7=0$, then the value of $2a+b+c-7$ is $\_\_\_\_\_\_$ .

3D Geometry

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