1
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
Equation of a plane at a distance $${2 \over {\sqrt {21} }}$$ from the origin, which contains the line of intersection of the planes x $$-$$ y $$-$$ z $$-$$ 1 = 0 and 2x + y $$-$$ 3z + 4 = 0, is :
A
$$3x - y - 5z + 2 = 0$$
B
$$3x - 4z + 3 = 0$$
C
$$- x + 2y + 2z - 3 = 0$$
D
$$4x - y - 5z + 2 = 0$$
2
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
Let P be the plane passing through the point (1, 2, 3) and the line of intersection of the planes $$\overrightarrow r \,.\,\left( {\widehat i + \widehat j + 4\widehat k} \right) = 16$$ and $$\overrightarrow r \,.\,\left( { - \widehat i + \widehat j + \widehat k} \right) = 6$$. Then which of the following points does NOT lie on P?
A
(3, 3, 2)
B
(6, $$-$$6, 2)
C
(4, 2, 2)
D
($$-$$8, 8, 6)
3
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
A plane P contains the line $$x + 2y + 3z + 1 = 0 = x - y - z - 6$$, and is perpendicular to the plane $$- 2x + y + z + 8 = 0$$. Then which of the following points lies on P?
A
($$-$$1, 1, 2)
B
(0, 1, 1)
C
(1, 0, 1)
D
(2, $$-$$1, 1)
4
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
For real numbers $$\alpha$$ and $$\beta$$ $$\ne$$ 0, if the point of intersection of the straight lines

$${{x - \alpha } \over 1} = {{y - 1} \over 2} = {{z - 1} \over 3}$$ and $${{x - 4} \over \beta } = {{y - 6} \over 3} = {{z - 7} \over 3}$$, lies on the plane x + 2y $$-$$ z = 8, then $$\alpha$$ $$-$$ $$\beta$$ is equal to :
A
5
B
9
C
3
D
7
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