1
JEE Main 2024 (Online) 9th April Evening Shift
+4
-1

Consider the line $$\mathrm{L}$$ passing through the points $$(1,2,3)$$ and $$(2,3,5)$$. The distance of the point $$\left(\frac{11}{3}, \frac{11}{3}, \frac{19}{3}\right)$$ from the line $$\mathrm{L}$$ along the line $$\frac{3 x-11}{2}=\frac{3 y-11}{1}=\frac{3 z-19}{2}$$ is equal to

A
6
B
3
C
5
D
4
2
JEE Main 2024 (Online) 9th April Morning Shift
+4
-1

The shortest distance between the lines $$\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5}$$ and $$\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1}$$ is:

A
$$\frac{185}{\sqrt{563}}$$
B
$$\frac{187}{\sqrt{563}}$$
C
$$\frac{178}{\sqrt{563}}$$
D
$$\frac{179}{\sqrt{563}}$$
3
JEE Main 2024 (Online) 9th April Morning Shift
+4
-1

Let the line $$\mathrm{L}$$ intersect the lines $$x-2=-y=z-1,2(x+1)=2(y-1)=z+1$$ and be parallel to the line $$\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}$$. Then which of the following points lies on $$\mathrm{L}$$ ?

A
$$\left(-\frac{1}{3}, 1,-1\right)$$
B
$$\left(-\frac{1}{3},-1,1\right)$$
C
$$\left(-\frac{1}{3},-1,-1\right)$$
D
$$\left(-\frac{1}{3}, 1,1\right)$$
4
JEE Main 2024 (Online) 8th April Evening Shift
+4
-1

If the shortest distance between the lines $$\frac{x-\lambda}{2}=\frac{y-4}{3}=\frac{z-3}{4}$$ and $$\frac{x-2}{4}=\frac{y-4}{6}=\frac{z-7}{8}$$ is $$\frac{13}{\sqrt{29}}$$, then a value of $$\lambda$$ is :

A
$$\frac{13}{25}$$
B
1
C
$$-$$1
D
$$-\frac{13}{25}$$
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