1
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

Let the plane P pass through the intersection of the planes $$2x+3y-z=2$$ and $$x+2y+3z=6$$, and be perpendicular to the plane $$2x+y-z+1=0$$. If d is the distance of P from the point ($$-$$7, 1, 1), then $$\mathrm{d^{2}}$$ is equal to :

A
$$\frac{250}{83}$$
B
$$\frac{250}{82}$$
C
$$\frac{15}{53}$$
D
$$\frac{25}{83}$$
2
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

The shortest distance between the lines

$${{x - 5} \over 1} = {{y - 2} \over 2} = {{z - 4} \over { - 3}}$$ and

$${{x + 3} \over 1} = {{y + 5} \over 4} = {{z - 1} \over { - 5}}$$ is :

A
$$7\sqrt 3$$
B
$$5\sqrt 3$$
C
$$4\sqrt 3$$
D
$$6\sqrt 3$$
3
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

Let the image of the point $$P(2,-1,3)$$ in the plane $$x+2 y-z=0$$ be $$Q$$. Then the distance of the plane $$3 x+2 y+z+29=0$$ from the point $$Q$$ is

A
$$2\sqrt{14}$$
B
$$\frac{22\sqrt2}{7}$$
C
$$\frac{24\sqrt2}{7}$$
D
$$3\sqrt{14}$$
4
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
Let the plane $\mathrm{P}: 8 x+\alpha_{1} y+\alpha_{2} z+12=0$ be parallel to

the line $\mathrm{L}: \frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}$. If the intercept of $\mathrm{P}$

on the $y$-axis is 1 , then the distance between $\mathrm{P}$ and $\mathrm{L}$ is :
A
$\frac{6}{\sqrt{14}}$
B
$\sqrt{14}$
C
$\sqrt{\frac{2}{7}}$
D
$\sqrt{\frac{7}{2}}$
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