1
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 _______________.

2
JEE Main 2022 (Online) 25th June Morning Shift
Numerical
+4
-1
Out of Syllabus

Let the lines

$${L_1}:\overrightarrow r = \lambda \left( {\widehat i + 2\widehat j + 3\widehat k} \right),\,\lambda \in R$$

$${L_2}:\overrightarrow r = \left( {\widehat i + 3\widehat j + \widehat k} \right) + \mu \left( {\widehat i + \widehat j + 5\widehat k} \right);\,\mu \in R$$,

intersect at the point S. If a plane ax + by $$-$$ z + d = 0 passes through S and is parallel to both the lines L1 and L2, then the value of a + b + d is equal to ____________.

3
JEE Main 2022 (Online) 24th June Morning Shift
Numerical
+4
-1

Let a line having direction ratios, 1, $$-$$4, 2 intersect the lines $${{x - 7} \over 3} = {{y - 1} \over { - 1}} = {{z + 2} \over 1}$$ and $${x \over 2} = {{y - 7} \over 3} = {z \over 1}$$ at the points A and B. Then (AB)2 is equal to ___________.

4
JEE Main 2022 (Online) 24th June Morning Shift
Numerical
+4
-1

If the shortest distance between the lines

$$\overrightarrow r = \left( { - \widehat i + 3\widehat k} \right) + \lambda \left( {\widehat i - a\widehat j} \right)$$

and $$\overrightarrow r = \left( { - \widehat j + 2\widehat k} \right) + \mu \left( {\widehat i - \widehat j + \widehat k} \right)$$ is $$\sqrt {{2 \over 3}}$$, then the integral value of a is equal to ___________.