1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Out of Syllabus
The distance of the point ($$-$$1, 2, $$-$$2) from the line of intersection of the planes 2x + 3y + 2z = 0 and x $$-$$ 2y + z = 0 is :
A
$${1 \over {\sqrt 2 }}$$
B
$${5 \over 2}$$
C
$${{\sqrt {42} } \over 2}$$
D
$${{\sqrt {34} } \over 2}$$
2
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
Out of Syllabus
Let the equation of the plane, that passes through the point (1, 4, $$-$$3) and contains the line of intersection of the
planes 3x $$-$$ 2y + 4z $$-$$ 7 = 0
and x + 5y $$-$$ 2z + 9 = 0, be
$$\alpha$$x + $$\beta$$y + $$\gamma$$z + 3 = 0, then $$\alpha$$ + $$\beta$$ + $$\gamma$$ is equal to :
A
$$-$$23
B
$$-$$15
C
23
D
15
3
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $$-$$ n = 0 and mn + nl + lm = 0, is :
A
$${\pi \over 2}$$
B
$$\pi - {\cos ^{ - 1}}\left( {{4 \over 9}} \right)$$
C
$${\cos ^{ - 1}}\left( {{8 \over 9}} \right)$$
D
$${\pi \over 3}$$
4
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Out of Syllabus
The equation of the plane passing through the line of intersection of the planes $$\overrightarrow r .\left( {\widehat i + \widehat j + \widehat k} \right) = 1$$ and $$\overrightarrow r .\left( {2\widehat i + 3\widehat j - \widehat k} \right) + 4 = 0$$ and parallel to the x-axis is :
A
$$\overrightarrow r .\left( {\widehat j - 3\widehat k} \right) + 6 = 0$$
B
$$\overrightarrow r .\left( {\widehat i + 3\widehat k} \right) + 6 = 0$$
C
$$\overrightarrow r .\left( {\widehat i - 3\widehat k} \right) + 6 = 0$$
D
$$\overrightarrow r .\left( {\widehat j - 3\widehat k} \right) - 6 = 0$$
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