List of top Mathematics Questions on Three Dimensional Geometry asked in JEE Main

If the foot is perpendicular from (1, 2, 3) to the line $\frac{x+1}{2} = \frac{y-2}{5} = \frac{z-1}{1}$ is $( a, \beta, \gamma)$, then find $a + \beta + \gamma$

Let the image of the point $P(2,-1,3)$ in the plane $x+2 y-z=0$ be $Q$ Then the distance of the plane $3 x+2 y+z+29=0$ from the point $Q$ is

The distance of the point $P (4,6,-2)$ from the line passing through the point $(-3,2,3)$ and parallel to a line with direction ratios $3,3,-1$ is equal to :

Let the line $L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2 x+y+3 z=16$ 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 $P Q R$, then $\alpha^2$ is equal to

Let $\alpha x+\beta y+y z=1$ 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 $\alpha \beta y$ is equal to ____

Shortest distance between lines $\frac{(x-5)}{4}$=$\frac{(y-3)}{6}$=$\frac{(z-2)}{4}$ and $\frac{(x-3)}{7}=\frac{(y-2)}{5}=\frac{(z-9)}{6}$ is ?

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

The distance of the point $(-1,9,-16)$ from the plane $2 x+3 y-z=5$ measured parallel to the line $\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}$ is

If $A(1, 1, 1), B(0, λ, 0), C(λ + 1, 0, 1), D(2, -2, 2)$ are co-planer then $\sum (\lambda_i + 2)^2$ is equal to

If the image of point P(1, 2, 3) about the plane 2x - y + 3z = 2 is Q, then the area of triangle PQR, where coordinates of R is (4, 10, 12)

Let the plane containing the line of intersection of the planes $P 1: x+(\lambda+4) y+z=1$ and $P 2: 2 x+$ $y+z=2$ pass through the points $(0,1,0)$ and $(1,0,1)$ Then the distance of the point $(2 \lambda, \lambda,-\lambda)$ from the plane $P 2$ is

Plane P₃ is passing through (1,1,1) and line of intersection of P₁ and P₂ where $P_{1}: 2x - y + z = 5$ and $P_{2}: x + 3y + 2z + 2 = 0$. Then distance of (1,1,10) from P₃ is:

A plane $E$ is perpendicular to the two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, and passes through the point $P (1,-1,1)$ If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3 \sqrt{2}$, then $( PQ )^2$ is equal to

A rectangular parallelepiped with edges along x, y, z axis has length 3, 4, 5 respectively. Fiind the shortest distance of the body diagonal from one of the edges parallel to z-axis which is skew to the diagonal

The point of intersection $C$ of the plane $8 x+y+2 z=0$ 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 ___

If $\lambda_1<\lambda_2$ are two values of $\lambda$ such that the angle between the planes $P_1: \vec{r}(3 \hat{i}-5 \hat{j}+\hat{k})=7$ and $P_2: \vec{r} \cdot(\lambda \hat{i}+\hat{j}-3 \hat{k})=9$ is $\sin ^{-1}\left(\frac{2 \sqrt{6}}{5}\right)$, then the square of the length of perpendicular from the point $\left(38 \lambda_1, 10 \lambda_2, 2\right)$ to the plane $P_1$ is _____

Let N be the foot of perpendicular from the point P (1, –2, 3) on the line passing through the points (4, 5, 8) and (1, –7, 5). Then the distance of N from the plane 2x – 2y + z + 5 = 0 is

The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parellel to the line passing through (5,1,-7) and (1,-1,-1), also passes through the point

The line, that is coplanar to the line $\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}$ is

Let the line / : x = $\frac{1-y}{2}=\frac{z-3}{\lambda}, \lambda \in R$ meet the plane P : x+2y +3z = 4 at the point $(\alpha, \beta, \lambda)$. If the angle between the line I and the plane P is $cos^{-1}\bigg(\sqrt{\frac{5}{14}}\bigg)$ then $\alpha+2\beta+6\lambda$ is equal to______.

Let $\theta$ be the angle between the planes $P_1: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9$ and $P_2: \hat{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=15$ Let $L$ be the line that meets $P_2$ at the point $(4,-2,5)$ and makes an angle $\theta$ with the normal of $P_4$ If $\alpha$ is the angle between $L$ and $P_2$, then $\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)$ is equal to

$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$is equal to

Let Q and R be two points on the line
$\frac{x+1}{2}=\frac{y+2}{3}=\frac{z−1}{2}$ at a distance $\sqrt{26}$
from the point P(4, 2, 7). Then the square of the area of the triangle PQR is _______ .

Let the plane
$P : \stackrel{→}{r} . \stackrel{→}{a} = d$
contain the line of intersection of two planes
$\stackrel{→}{r} . ( \hat{i} + 3\hat{j} - \hat{k} ) = 6$
and
$\stackrel{→}{r} . ( -6\hat{i} + 5\hat{j} - \hat{k} ) = 7$
. If the plane P passes through the point (2, 3, 1/2),
then the value of $\frac{| 13a→|² }{d²}$ is equal to

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line
$\vec{r}=−\hat{k}+λ(\hat{i}+\hat{j}+2\hat{k}), λ ∈ R.$
Then, which of the following points lies on T?

List of top Mathematics Questions on Three Dimensional Geometry asked in JEE Main

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