1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

Let p be the plane passing through the intersection of the planes $$\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 5$$ and $$\overrightarrow r \,.\,\left( {2\widehat i - \widehat j + \widehat k} \right) = 3$$, and the point (2, 1, $$-$$2). Let the position vectors of the points X and Y be $$\widehat i - 2\widehat j + 4\widehat k$$ and $$5\widehat i - \widehat j + 2\widehat k$$ respectively. Then the points

A
X and X + Y are on the same side of P
B
Y and Y $$-$$ X are on the opposite sides of P
C
X and Y are on the opposite sides of P
D
X + Y and X $$-$$ Y are on the same side of P
2
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y + z = 5. If a line L passing through (1, $$-$$1, $$-$$1), parallel to the line PQ meets the plane S at R, then QR2 is equal to :

A
2
B
5
C
7
D
11
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

If the shortest distance between the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over \lambda }$$ and $${{x - 2} \over 1} = {{y - 4} \over 4} = {{z - 5} \over 5}$$ is $${1 \over {\sqrt 3 }}$$, then the sum of all possible value of $$\lambda$$ is :

A
16
B
6
C
12
D
15
4
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Let the points on the plane P be equidistant from the points ($$-$$4, 2, 1) and (2, $$-$$2, 3). Then the acute angle between the plane P and the plane 2x + y + 3z = 1 is

A
$${\pi \over 6}$$
B
$${\pi \over 4}$$
C
$${\pi \over 3}$$
D
$${5\pi \over 12}$$
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