1
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

Let $$Q$$ be the foot of perpendicular drawn from the point $$P(1,2,3)$$ to the plane $$x+2 y+z=14$$. If $$R$$ is a point on the plane such that $$\angle P R Q=60^{\circ}$$, then the area of $$\triangle P Q R$$ is equal to :

A
$$\frac{\sqrt{3}}{2}$$
B
$$\sqrt{3}$$
C
$$2 \sqrt{3}$$
D
3
2
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

If $$(2,3,9),(5,2,1),(1, \lambda, 8)$$ and $$(\lambda, 2,3)$$ are coplanar, then the product of all possible values of $$\lambda$$ is:

A
$$\frac{21}{2}$$
B
$$\frac{59}{8}$$
C
$$\frac{57}{8}$$
D
$$\frac{95}{8}$$
3
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

If the foot of the perpendicular from the point $$\mathrm{A}(-1,4,3)$$ on the plane $$\mathrm{P}: 2 x+\mathrm{m} y+\mathrm{n} z=4$$, is $$\left(-2, \frac{7}{2}, \frac{3}{2}\right)$$, then the distance of the point A from the plane P, measured parallel to a line with direction ratios $$3,-1,-4$$, is equal to :

A
1
B
$$\sqrt{26}$$
C
2$$\sqrt{2}$$
D
$$\sqrt{14}$$
4
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Let the lines $$\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$$ and $$\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}$$ be coplanar and $$\mathrm{P}$$ be the plane containing these two lines. Then which of the following points does NOT lie on P?

A
$$(0,-2,-2)$$
B
$$(-5,0,-1)$$
C
$$(3,-1,0)$$
D
$$(0,4,5)$$
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