1
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1

Consider the lines $$L_1$$ and $$L_2$$ given by

$${L_1}:{{x - 1} \over 2} = {{y - 3} \over 1} = {{z - 2} \over 2}$$

$${L_2}:{{x - 2} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$$.

A line $$L_3$$ having direction ratios 1, $$-$$1, $$-$$2, intersects $$L_1$$ and $$L_2$$ at the points $$P$$ and $$Q$$ respectively. Then the length of line segment $$PQ$$ is

A
$$4\sqrt3$$
B
$$2\sqrt6$$
C
4
D
$$3\sqrt2$$
2
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1
Out of Syllabus

If the foot of the perpendicular drawn from (1, 9, 7) to the line passing through the point (3, 2, 1) and parallel to the planes $$x+2y+z=0$$ and $$3y-z=3$$ is ($$\alpha,\beta,\gamma$$), then $$\alpha+\beta+\gamma$$ is equal to :

A
3
B
1
C
$$-$$1
D
5
3
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1
Out of Syllabus

Let the plane containing the line of intersection of the planes

P1 : $$x+(\lambda+4)y+z=1$$ and

P2 : $$2x+y+z=2$$

pass through the points (0, 1, 0) and (1, 0, 1). Then the distance of

the point (2$$\lambda,\lambda,-\lambda$$) from the plane P2 is :

A
$$2\sqrt6$$
B
$$3\sqrt6$$
C
$$4\sqrt6$$
D
$$5\sqrt6$$
4
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1
Out of Syllabus

The distance of the point (7, $$-$$3, $$-$$4) from the plane passing through the points (2, $$-$$3, 1), ($$-$$1, 1, $$-$$2) and (3, $$-$$4, 2) is :

A
$$4\sqrt2$$
B
4
C
5
D
$$5\sqrt2$$
EXAM MAP
Medical
NEET