The equation of the plane passing through the line of intersection of the planes $$\overrightarrow r .\left( {\widehat i + \widehat j + \widehat k} \right) = 1$$ and $$\overrightarrow r .\left( {2\widehat i + 3\widehat j - \widehat k} \right) + 4 = 0$$ and parallel to the x-axis is :
$$ \Rightarrow \overrightarrow r .\left( {\widehat j - 3\widehat k} \right) + 6 = 0$$ Ans.
2
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
Equation of a plane at a distance $${2 \over {\sqrt {21} }}$$ from the origin, which contains the line of intersection of the planes x $$-$$ y $$-$$ z $$-$$ 1 = 0 and 2x + y $$-$$ 3z + 4 = 0, is :
A
$$3x - y - 5z + 2 = 0$$
B
$$3x - 4z + 3 = 0$$
C
$$ - x + 2y + 2z - 3 = 0$$
D
$$4x - y - 5z + 2 = 0$$
Explanation
Required equation of plane
$${P_1} + \lambda {P_2} = 0$$
$$(x - y - z - 1) + \lambda (2x + y - 3z + 4) = 0$$
Given that its dist. From origin is $${2 \over {\sqrt {21} }}$$
for $$\lambda = {1 \over 2}$$ reqd. plane is $$4x - y - 5z + 2 = 0$$
3
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
Let P be the plane passing through the point (1, 2, 3) and the line of intersection of the planes $$\overrightarrow r \,.\,\left( {\widehat i + \widehat j + 4\widehat k} \right) = 16$$ and $$\overrightarrow r \,.\,\left( { - \widehat i + \widehat j + \widehat k} \right) = 6$$. Then which of the following points does NOT lie on P?
A
(3, 3, 2)
B
(6, $$-$$6, 2)
C
(4, 2, 2)
D
($$-$$8, 8, 6)
Explanation
$$(x + y + 4z - 16) + \lambda ( - x + y + z - 6) = 0$$
A hall has a square floor of dimension 10 m $$\times$$ 10 m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is $${\cos ^{ - 1}}{1 \over 5}$$, then the height of the hall (in meters) is :