3D Geometry

Showing 46-50 of 461 questions.

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JEE Main 2023 (Online) 11th April Evening ShiftQuestion 46

Let $P$ be the plane passing through the points $(5,3,0)$, $(13,3,-2)$ and $(1,6,2)$. For $\alpha\in\mathbb{N}$, if the distances of the points $A(3,4,\alpha)$ and $B(2,\alpha,a)$ from the plane $P$ are $2$ and $3$ respectively, then the positive value of $a$ is

3D Geometry

$3$$4$$5$$6$

JEE Main 2023 (Online) 6th April Evening ShiftQuestion 47

Let the line $L$ pass through the point $(0,1,2)$, intersect the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and be parallel to the plane $2x+y-3z=4$. Then the distance of the point $P(1,-9,2)$ from the line $L$ is

3D Geometry

$\sqrt{54}$$\sqrt{69}$$\sqrt{74}$$9$

JEE Main 2023 (Online) 8th April Morning ShiftQuestion 48

If the equation of the plane containing the line $x+2y+3z-4=0=2x+y-z+5$ and perpendicular to the plane $\vec{r}=\left(\hat{i}-\hat{j}\right)+\lambda\left(\hat{i}+\hat{j}+\hat{k}\right)+\mu\left(\hat{i}-2\hat{j}+3\hat{k}\right)$ is $ax+by+cz=4$, then $(a-b+c)$ is equal to

3D Geometry

$18$$20$$22$$24$

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 49

A plane intersects the $yz$-plane at $x=0$, $2y-3z=5$ and it intersects the $xy$-plane at $z=0$, $7x+4y=10$. Then the distance of the point $(1,-2,-1)$ from this plane is

3D Geometry

$\frac{1}{\sqrt{101}}$$\frac{3}{\sqrt{101}}$$\frac{5}{\sqrt{101}}$$\frac{7}{\sqrt{101}}$

JEE Main 2021 (Online) 31st August Evening ShiftQuestion 50

The distance of the point $(-1,2,-2)$ from the line of intersection of the planes $2x+3y+2z=0$ and $x-2y+z=0$ is :

3D Geometry

$\frac{1}{\sqrt{2}}$$\frac{5}{2}$$\frac{\sqrt{34}}{2}$$\frac{\sqrt{42}}{2}$