1
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The distance of the point P(4, 6, $$-$$2) from the line passing through the point ($$-$$3, 2, 3) and parallel to a line with direction ratios 3, 3, $$-$$1 is equal to :

A
3
B
$$\sqrt{14}$$
C
$$\sqrt6$$
D
$$2\sqrt3$$
2
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$$3\sqrt2$$
3
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

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
4
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

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
$$5\sqrt6$$
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