1
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1
Out of Syllabus

Let the line passing through the points $$\mathrm{P}(2,-1,2)$$ and $$\mathrm{Q}(5,3,4)$$ meet the plane $$x-y+z=4$$ at the point $$\mathrm{R}$$. Then the distance of the point $$\mathrm{R}$$ from the plane $$x+2 y+3 z+2=0$$ measured parallel to the line $$\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}$$ is equal to :

A
$$\sqrt{31}$$
B
$$\sqrt{189}$$
C
$$\sqrt{61}$$
D
3
2
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1
Out of Syllabus

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 $$\mathrm{A}(3,4, \alpha)$$ and $$\mathrm{B}(2, \alpha, a)$$ from the plane P are 2 and 3 respectively, then the positive value of a is :

A
6
B
4
C
5
D
3
3
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1
Out of Syllabus

Let $$(\alpha, \beta, \gamma)$$ be the image of the point $$\mathrm{P}(2,3,5)$$ in the plane $$2 x+y-3 z=6$$. Then $$\alpha+\beta+\gamma$$ is equal to :

A
10
B
9
C
5
D
12
4
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1
Out of Syllabus

If equation of the plane that contains the point $$(-2,3,5)$$ and is perpendicular to each of the planes $$2 x+4 y+5 z=8$$ and $$3 x-2 y+3 z=5$$ is $$\alpha x+\beta y+\gamma z+97=0$$ then $$\alpha+\beta+\gamma=$$

A
15
B
16
C
17
D
18
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