1
JEE Main 2022 (Online) 29th June Morning Shift
Numerical
+4
-1
Out of Syllabus

Let $${P_1}:\overrightarrow r \,.\,\left( {2\widehat i + \widehat j - 3\widehat k} \right) = 4$$ be a plane. Let P2 be another plane which passes through the points (2, $$-$$3, 2), (2, $$-$$2, $$-$$3) and (1, $$-$$4, 2). If the direction ratios of the line of intersection of P1 and P2 be 16, $$\alpha$$, $$\beta$$, then the value of $$\alpha$$ + $$\beta$$ is equal to ________________.

2
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1

Let the image of the point P(1, 2, 3) in the line $$L:{{x - 6} \over 3} = {{y - 1} \over 2} = {{z - 2} \over 3}$$ be Q. Let R ($$\alpha$$, $$\beta$$, $$\gamma$$) be a point that divides internally the line segment PQ in the ratio 1 : 3. Then the value of 22 ($$\alpha$$ + $$\beta$$ + $$\gamma$$) is equal to __________.

3
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Out of Syllabus

Let the mirror image of the point (a, b, c) with respect to the plane 3x $$-$$ 4y + 12z + 19 = 0 be (a $$-$$ 6, $$\beta$$, $$\gamma$$). If a + b + c = 5, then 7$$\beta$$ $$-$$ 9$$\gamma$$ is equal to ______________.

4
JEE Main 2022 (Online) 25th June Evening Shift
Numerical
+4
-1

Let l1 be the line in xy-plane with x and y intercepts $${1 \over 8}$$ and $${1 \over {4\sqrt 2 }}$$ respectively, and l2 be the line in zx-plane with x and z intercepts $$- {1 \over 8}$$ and $$- {1 \over {6\sqrt 3 }}$$ respectively. If d is the shortest distance between the line l1 and l2, then d$$-$$2 is equal to _______________.