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

The foot of perpendicular of the point (2, 0, 5) on the line $${{x + 1} \over 2} = {{y - 1} \over 5} = {{z + 1} \over { - 1}}$$ is ($$\alpha,\beta,\gamma$$). Then, which of the following is NOT correct?

A
$$\frac{\alpha}{\beta}=-8$$
B
$$\frac{\alpha \beta}{\gamma}=\frac{4}{15}$$
C
$$\frac{\beta}{\gamma}=-5$$
D
$$\frac{\gamma}{\alpha}=\frac{5}{8}$$
2
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

The shortest distance between the lines $$x+1=2y=-12z$$ and $$x=y+2=6z-6$$ is :

A
3
B
$$\frac{5}{2}$$
C
$$\frac{3}{2}$$
D
2
3
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1

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
$$2\sqrt3$$
4
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
$$3\sqrt2$$
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