1
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
2
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
$${5\pi \over 12}$$
3
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Let the acute angle bisector of the two planes x $$-$$ 2y $$-$$ 2z + 1 = 0 and 2x $$-$$ 3y $$-$$ 6z + 1 = 0 be the plane P. Then which of the following points lies on P?
A
$$\left( {3,1, - {1 \over 2}} \right)$$
B
$$\left( { - 2,0, - {1 \over 2}} \right)$$
C
(0, 2, $$-$$4)
D
(4, 0, $$-$$2)
4
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
The distance of line $$3y - 2z - 1 = 0 = 3x - z + 4$$ from the point (2, $$-$$1, 6) is :
A
$$\sqrt {26}$$
B
$$2\sqrt 5$$
C
$$2\sqrt 6$$
D
$$4\sqrt 2$$
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