1
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
$${\pi \over 3}$$
2
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
$$\overrightarrow r .\left( {\widehat j - 3\widehat k} \right) - 6 = 0$$
3
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
Out of Syllabus
The distance of the point (1, $$-$$2, 3) from the plane x $$-$$ y + z = 5 measured parallel to a line, whose direction ratios are 2, 3, $$-$$6 is :
A
3
B
5
C
2
D
1
4
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
Out of Syllabus
Equation of a plane at a distance $$\sqrt {{2 \over {21}}}$$ from the origin, which contains the line of intersection of the planes x $$-$$ y $$-$$ z $$-$$ 1 = 0 and 2x + y $$-$$ 3z + 4 = 0, is :
A
$$3x - y - 5z + 2 = 0$$
B
$$3x - 4z + 3 = 0$$
C
$$- x + 2y + 2z - 3 = 0$$
D
$$4x - y - 5z + 2 = 0$$
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