1
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

The length of the perpendicular from the point $$(1,-2,5)$$ on the line passing through $$(1,2,4)$$ and parallel to the line $$x+y-z=0=x-2 y+3 z-5$$ is :

A
$$\sqrt{\frac{21}{2}}$$
B
$$\sqrt{\frac{9}{2}}$$
C
$$\sqrt{\frac{73}{2}}$$
D
1
2
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1

A plane $$E$$ is perpendicular to the two planes $$2 x-2 y+z=0$$ and $$x-y+2 z=4$$, and passes through the point $$P(1,-1,1)$$. If the distance of the plane $$E$$ from the point $$Q(a, a, 2)$$ is $$3 \sqrt{2}$$, then $$(P Q)^{2}$$ is equal to

A
9
B
12
C
21
D
33
3
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1

The shortest distance between the lines $$\frac{x+7}{-6}=\frac{y-6}{7}=z$$ and $$\frac{7-x}{2}=y-2=z-6$$ is

A
$$2 \sqrt{29}$$
B
1
C
$$\sqrt{\frac{37}{29}}$$
D
$$\frac{\sqrt{29}}{2}$$
4
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

Let $$\mathrm{P}$$ be the plane containing the straight line $$\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$$ and perpendicular to the plane containing the straight lines $$\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$$ and $$\frac{x}{3}=\frac{y}{7}=\frac{z}{8}$$. If $$\mathrm{d}$$ is the distance of $$\mathrm{P}$$ from the point $$(2,-5,11)$$, then $$\mathrm{d}^{2}$$ is equal to :

A
$$\frac{147}{2}$$
B
96
C
$$\frac{32}{3}$$
D
54
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