1
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

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

A
$$\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z-5}{4}$$
B
$$\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z-5}{5}$$
C
$$\frac{x-1}{-1}=\frac{y-2}{2}=\frac{z-5}{5}$$
D
$$\frac{x+1}{1}=\frac{y-2}{2}=\frac{z-5}{5}$$
2
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

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

A
$$(0,5,-2)$$
B
$$(2,0,1)$$
C
$$(1,-2,1)$$
D
$$(-2,5,0)$$
3
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

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

A
7
B
6
C
9
D
8
4
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

Let the equation of plane passing through the line of intersection of the planes $$x+2 y+a z=2$$ and $$x-y+z=3$$ be $$5 x-11 y+b z=6 a-1$$. For $$c \in \mathbb{Z}$$, if the distance of this plane from the point $$(a,-c, c)$$ is $$\frac{2}{\sqrt{a}}$$, then $$\frac{a+b}{c}$$ is equal to :

A
$$-$$2
B
4
C
2
D
$$-$$4
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