1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1
Out of Syllabus

If the plane $$P$$ passes through the intersection of two mutually perpendicular planes $$2 x+k y-5 z=1$$ and $$3 k x-k y+z=5, k<3$$ and intercepts a unit length on positive $$x$$-axis, then the intercept made by the plane $$P$$ on the $$y$$-axis is :

A
$$\frac{1}{11}$$
B
$$\frac{5}{11}$$
C
6
D
7
2
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1
Out of Syllabus

A vector $$\vec{a}$$ is parallel to the line of intersection of the plane determined by the vectors $$\hat{i}, \hat{i}+\hat{j}$$ and the plane determined by the vectors $$\hat{i}-\hat{j}, \hat{i}+\hat{k}$$. The obtuse angle between $$\vec{a}$$ and the vector $$\vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}$$ is :

A
$$\frac{3 \pi}{4}$$
B
$$\frac{2 \pi}{3}$$
C
$$\frac{4 \pi}{5}$$
D
$$\frac{5 \pi}{6}$$
3
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
4
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1
Out of Syllabus

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
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