1
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

Let the foot of the perpendicular from the point (1, 2, 4) on the line $${{x + 2} \over 4} = {{y - 1} \over 2} = {{z + 1} \over 3}$$ be P. Then the distance of P from the plane $$3x + 4y + 12z + 23 = 0$$ is

A
5
B
$${{50} \over {13}}$$
C
4
D
$${{63} \over {13}}$$
2
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

The shortest distance between the lines

$${{x - 3} \over 2} = {{y - 2} \over 3} = {{z - 1} \over { - 1}}$$ and $${{x + 3} \over 2} = {{y - 6} \over 1} = {{z - 5} \over 3}$$, is

A
$${{18} \over {\sqrt 5 }}$$
B
$${{22} \over {3\sqrt 5 }}$$
C
$${{46} \over {3\sqrt 5 }}$$
D
$$6\sqrt 3$$
3
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

If the plane $$2x + y - 5z = 0$$ is rotated about its line of intersection with the plane $$3x - y + 4z - 7 = 0$$ by an angle of $${\pi \over 2}$$, then the plane after the rotation passes through the point :

A
(2, $$-$$2, 0)
B
($$-$$2, 2, 0)
C
(1, 0, 2)
D
($$-$$1, 0, $$-$$2)
4
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

If the lines $$\overrightarrow r = \left( {\widehat i - \widehat j + \widehat k} \right) + \lambda \left( {3\widehat j - \widehat k} \right)$$ and $$\overrightarrow r = \left( {\alpha \widehat i - \widehat j} \right) + \mu \left( {2\widehat i - 3\widehat k} \right)$$ are co-planar, then the distance of the plane containing these two lines from the point ($$\alpha$$, 0, 0) is :

A
$${2 \over 9}$$
B
$${2 \over 11}$$
C
$${4 \over 11}$$
D
2
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