JEE Advanced 2021 Paper 1Question 411
The value of $D$ is ___ .
3D Geometry
JEE Mathematics / Practice
3D Geometry
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Comprehension · Questions 411–411
Read the passage given below and answer the questions that follow.
Let $\alpha,\beta$ and $\gamma$ be real numbers such that the system of linear equations
$$x+2y+3z=\alpha$$
$$4x+5y+6z=\beta$$
$$7x+8y+9z=\gamma-1$$
is consistent. Let $|M|$ represent the determinant of the matrix
$$M=\begin{bmatrix}\alpha&2&\gamma\\ \beta&1&0\\ -1&0&1\end{bmatrix}$$
Let $P$ be the plane containing all those $(\alpha,\beta,\gamma)$ for which the above system of linear equations is consistent, and $D$ be the square of the distance of the point $(0,1,0)$ from the plane $P$.
AIEEE 2012 (Offline) 29th April Code AQuestion 412
An equation of a plane parallel to the plane $x-2y+2z-5=0$ and at a unit distance from the origin is :
3D Geometry
AIEEE 2012 (Offline) 29th April Code AQuestion 413
If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac z1$ intersect, then $k$ is equal to :
3D Geometry
IIT-JEE 2004Question 414
$P_1$ and $P_2$ are planes passing through the origin. $L_1$ and $L_2$ are two lines on $P_1$ and $P_2$ respectively such that their intersection is the origin. Show that there exist points $A,B,C$, whose permutation $A',B',C'$ can be chosen such that (i) $A$ is on $L_1$, $B$ on $P_1$ but not on $L_1$ and $C$ not on $P_1$; (ii) $A'$ is on $L_2$, $B'$ on $P_2$ but not on $L_2$ and $C'$ not on $P_2$.
3D Geometry
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JEE Main 2021 (Online) 4th August Evening ShiftQuestion 415
The equation of a line passing through the point $(2,-1,1)$ and the point of intersection of the lines $2x-y-4=0=y+2z$ and $x+3z=0=2x+5z-1$, is
3D Geometry