1
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1

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

A
$$3 \sqrt{6}$$
B
$$6 \sqrt{2}$$
C
$$6 \sqrt{3}$$
D
$$2 \sqrt{6}$$
2
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1
Out of Syllabus

If the equation of the plane containing the line

$$x+2 y+3 z-4=0=2 x+y-z+5$$ and perpendicular to the plane

$\vec{r}=(\hat{i}-\hat{j})+\lambda(\hat{i}+\hat{j}+\hat{k})+\mu(\hat{i}-2 \hat{j}+3 \hat{k})$

is $a x+b y+c z=4$, then $$(a-b+c)$$ is equal to :

A
18
B
22
C
20
D
24
3
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1
Out of Syllabus

A plane P contains the line of intersection of the plane $$\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=6$$ and $$\vec{r} \cdot(2 \hat{i}+3 \hat{j}+4 \hat{k})=-5$$. If $$\mathrm{P}$$ passes through the point $$(0,2,-2)$$, then the square of distance of the point $$(12,12,18)$$ from the plane $$\mathrm{P}$$ is :

A
310
B
620
C
1240
D
155
4
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1
Out of Syllabus

Let the line $$\mathrm{L}$$ pass through the point $$(0,1,2)$$, intersect the line $$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$$ and be parallel to the plane $$2 x+y-3 z=4$$. Then the distance of the point $$\mathrm{P}(1,-9,2)$$ from the line $$\mathrm{L}$$ is :

A
9
B
$$\sqrt{74}$$
C
$$\sqrt{69}$$
D
$$\sqrt{54}$$
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