1
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1
Out of Syllabus

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)
2
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1
Out of Syllabus

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
3
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

Let $$\overrightarrow a = \widehat i + \widehat j + 2\widehat k$$, $$\overrightarrow b = 2\widehat i - 3\widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i - \widehat j + \widehat k$$ be three given vectors. Let $$\overrightarrow v$$ be a vector in the plane of $$\overrightarrow a$$ and $$\overrightarrow b$$ whose projection on $$\overrightarrow c$$ is $${2 \over {\sqrt 3 }}$$. If $$\overrightarrow v \,.\,\widehat j = 7$$, then $$\overrightarrow v \,.\,\left( {\widehat i + \widehat k} \right)$$ is equal to :

A
6
B
7
C
8
D
9
4
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

If the two lines $${l_1}:{{x - 2} \over 3} = {{y + 1} \over {-2}},\,z = 2$$ and $${l_2}:{{x - 1} \over 1} = {{2y + 3} \over \alpha } = {{z + 5} \over 2}$$ are perpendicular, then an angle between the lines l2 and $${l_3}:{{1 - x} \over 3} = {{2y - 1} \over { - 4}} = {z \over 4}$$ is :

A
$${\cos ^{ - 1}}\left( {{{29} \over 4}} \right)$$
B
$${\sec ^{ - 1}}\left( {{{29} \over 4}} \right)$$
C
$${\cos ^{ - 1}}\left( {{2 \over {29}}} \right)$$
D
$${\cos ^{ - 1}}\left( {{2 \over {\sqrt {29} }}} \right)$$
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