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

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) 27th June Morning Shift
+4
-1

If two straight lines whose direction cosines are given by the relations $$l + m - n = 0$$, $$3{l^2} + {m^2} + cnl = 0$$ are parallel, then the positive value of c is :

A
6
B
4
C
3
D
2
4
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)
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