JEE Mathematics / Practice

3D Geometry

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JEE Main 2023 (Online) 25th January Morning ShiftQuestion 341

Let the equation of the plane passing through the line $x-2y-z-5=0=x+y+3z-5$ and parallel to the line $x+y+2z-7=0=2x+3y+z-2$ be $ax+by+cz=65$. Then the distance of the point $(a,b,c)$ from the plane $2x+2y-z+16=0$ is

3D Geometry

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JEE Main 2023 (Online) 24th January Morning ShiftQuestion 342

The shortest distance between the lines $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-6}{2}$ and $\frac{x-6}{3}=\frac{1-y}{2}=\frac{z+8}{0}$ is equal to ______

3D Geometry

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JEE Main 2023 (Online) 29th January Morning ShiftQuestion 343

Let the co-ordinates of one vertex of $\triangle ABC$ be $A(0,2,\alpha)$ and the other two vertices lie on the line $\frac{x+\alpha}{5}=\frac{y-1}{2}=\frac{z+4}{3}$. For $\alpha\in\mathbb Z$, if the area of $\triangle ABC$ is $21$ sq. units and the line segment $BC$ has length $2\sqrt{21}$ units, then $\alpha^{2}$ is equal to ______.

3D Geometry

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JEE Main 2020 (Online) 7th January Evening ShiftQuestion 344

If the foot of the perpendicular drawn from the point $(1,0,3)$ on a line passing through $(\alpha,7,1)$ is $\left(\frac53,\frac73,\frac{17}3\right)$, then $\alpha$ is equal to

3D Geometry

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JEE Main 2023 (Online) 1st February Morning ShiftQuestion 345

$A(2,6,2)$, $B(-4,0,\lambda)$, $C(2,3,-1)$ and $D(4,5,0)$, $|\lambda|\le5$ are the vertices of a quadrilateral $ABCD$. If its area is $18$ square units, then $5-6\lambda$ is equal to ______.

3D Geometry

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