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Yukti Vault

JEE Mathematics / Practice

3D Geometry

Chapter overview and full question list

Showing 336-340 of 461 questions.

JEE Main 2023 (Online) 1st February Evening ShiftQuestion 336
Let $\alpha x+\beta y+\gamma z=1$ be the equation of a plane passing through the point $(3,-2,5)$ and perpendicular to the line joining the points $(1,2,3)$ and $(-2,3,5)$. Then the value of $\alpha\beta\gamma$ is equal to
3D Geometry
JEE Main 2023 (Online) 30th January Morning ShiftQuestion 337
If the equation of the plane passing through the point $(1,1,2)$ and perpendicular to the line $x-3y+2z-1=0=4x-y+z$ is $Ax+By+Cz=1$, then $140(C-B+A)$ is equal to ______.
3D Geometry
JEE Main 2023 (Online) 25th January Evening ShiftQuestion 338
If the shortest distance between the line joining the points $(1,2,3)$ and $(2,3,4)$, and the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-2}{0}$ is $\alpha$, then $28\alpha^2$ is equal to _____.
3D Geometry
JEE Main 2023 (Online) 1st February Evening ShiftQuestion 339
The point of intersection $C$ of the plane $8x+y+2z=0$ and the line joining the points $A(-3,-6,1)$ and $B(2,4,-3)$ divides the line segment $AB$ internally in the ratio $k:1$. If $a,b,c$ ($|a|,|b|,|c|$ are coprime) are the direction ratios of the perpendicular from the point $C$ on the line $\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}$, then $|a+b+c|$ is equal to
3D Geometry
JEE Main 2023 (Online) 31st January Morning ShiftQuestion 340
Let the line $L:\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2x+y+3z=16$ at the point $P$. Let the point $Q$ be the foot of perpendicular from the point $R(1,-1,-3)$ on the line $L$. If $\alpha$ is the area of triangle $PQR$, then $\alpha^{2}$ is equal to ______.
3D Geometry