3D Geometry

Showing 91-95 of 461 questions.

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JEE Main 2025 (Online) 7th April Evening ShiftQuestion 91

Consider the lines $L_1:x-1=y-2=z$ and $L_2:x-2=y=z-1$. Let the feet of the perpendiculars from the point $P(5,1,-3)$ on the lines $L_1$ and $L_2$ be $Q$ and $R$ respectively. If the area of the triangle $PQR$ is $A$, then $4A^{2}$ is equal to :

3D Geometry

$139$$143$$147$$151$

JEE Main 2022 (Online) 26th June Evening ShiftQuestion 92

If the plane $2x+y-5z=0$ is rotated about its line of intersection with the plane $3x-y+4z-7=0$ by an angle of $\frac{\pi}{2}$, then the plane after the rotation passes through the point :

3D Geometry

$(2,-2,0)$$(-2,2,0)$$(1,0,2)$$(-1,0,-2)$

JEE Main 2025 (Online) 7th April Morning ShiftQuestion 93

Let the line $L$ pass through $(1,1,1)$ and intersect the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z}{1}$. Then, which of the following points lies on the line $L$?

3D Geometry

$(4,22,7)$$(7,15,13)$$(10,-29,-50)$$(5,4,3)$

JEE Main 2024 (Online) 1st February Evening ShiftQuestion 94

Let $P$ and $Q$ be the points on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ which are at a distance of $6$ units from the point $R(1,2,3)$. If the centroid of the triangle $PQR$ is $(\alpha,\beta,\gamma)$, then $\alpha^{2}+\beta^{2}+\gamma^{2}$ is :

3D Geometry

$18$$24$$26$$36$

JEE Main 2025 (Online) 4th April Morning ShiftQuestion 95

Let the shortest distance between the lines $\frac{x-3}{3}=\frac{y-\alpha}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-\beta}{4}$ be $3\sqrt{30}$. Then the positive value of $5\alpha+\beta$ is

3D Geometry

$40$$42$$46$$48$