1
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
2
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

The distance of the point (3, 2, $$-$$1) from the plane $$3x - y + 4z + 1 = 0$$ along the line $${{2 - x} \over 2} = {{y - 3} \over 2} = {{z + 1} \over 1}$$ is equal to :

A
9
B
6
C
3
D
2
3
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1

Let $${{x - 2} \over 3} = {{y + 1} \over { - 2}} = {{z + 3} \over { - 1}}$$ lie on the plane $$px - qy + z = 5$$, for some p, q $$\in$$ R. The shortest distance of the plane from the origin is :

A
$$\sqrt {{3 \over {109}}}$$
B
$$\sqrt {{5 \over {142}}}$$
C
$${5 \over {\sqrt {71} }}$$
D
$${1 \over {\sqrt {142} }}$$
4
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line $$\overrightarrow r = - \widehat k + \lambda \left( {\widehat i + \widehat j + 2\widehat k} \right),\,\lambda \in R$$. Then, which of the following points lies on T ?

A
(2, 1, 0)
B
(1, 2, 1)
C
(1, 2, 2)
D
(1, 3, 2)
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