3D Geometry

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JEE Main 2021 (Online) 3rd August Morning ShiftQuestion 41

The plane which is parallel to $\vec{r}\cdot\left(\hat{i}+2\hat{j}+3\hat{k}\right)=6$ and passes through $(1,2,3)$, also passes through the point

3D Geometry

$(2,6,1)$$(2,6,0)$$(3,6,-1)$$(3,5,1)$

JEE Main 2023 (Online) 8th April Evening ShiftQuestion 42

For $a,b\in\mathbb{Z}$ and $|a-b|\le10$, let the angle between the plane $P:ax+y-z=b$ and the line $l:x-1=a-y=z+1$ be $\cos^{-1}\left(\frac{1}{3}\right)$. If the distance of the point $(6,-6,4)$ from the plane $P$ is $3\sqrt{6}$, then $a^{4}+b^{2}$ is equal to

3D Geometry

$25$$32$$48$$85$

JEE Main 2021 (Online) 16th March Evening ShiftQuestion 43

If $(x,y,z)$ be an arbitrary point lying on a plane $P$ which passes through the points $(42,0,0)$, $(0,42,0)$ and $(0,0,42)$, then the value of the expression $3+\frac{x-11}{(y-19)^{2}(z-12)^{2}}+\frac{y-19}{(x-11)^{2}(z-12)^{2}}+\frac{z-12}{(x-11)^{2}(y-19)^{2}}-\frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is equal to :

3D Geometry

$-45$$39$$0$$3$

JEE Main 2021 (Online) 26th February Morning ShiftQuestion 44

Consider the three planes $P_1:3x+15y+21z=9$, $P_2:x-3y-z=5$, and $P_3:2x+10y+14z=5$ Then, which one of the following is true ?

3D Geometry

$P_1$ and $P_2$ are parallel.$P_1$ and $P_3$ are parallel.$P_1,P_2$ and $P_3$ all are parallel.$P_2$ and $P_3$ are parallel.

JEE Main 2023 (Online) 10th April Morning ShiftQuestion 45

Let two vertices of a triangle $ABC$ be $(2,4,6)$ and $(0,-2,-5)$, and its centroid be $(2,1,-1)$. If the image of the third vertex in the plane $x+2y+4z=11$ is $(\alpha,\beta,\gamma)$, then $\alpha\beta+\beta\gamma+\gamma\alpha$ is equal to

3D Geometry

$70$$72$$74$$76$