1
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 ___________.

2
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 ___________.

3
JEE Main 2021 (Online) 31st August Evening Shift
Numerical
+4
-1
Out of Syllabus
Suppose, the line $${{x - 2} \over \alpha } = {{y - 2} \over { - 5}} = {{z + 2} \over 2}$$ lies on the plane $$x + 3y - 2z + \beta = 0$$. Then $$(\alpha + \beta )$$ is equal to _______.
4
JEE Main 2021 (Online) 31st August Morning Shift
Numerical
+4
-1
Out of Syllabus
The square of the distance of the point of intersection

of the line $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z + 1} \over 6}$$ and the plane $$2x - y + z = 6$$ from the point ($$-$$1, $$-$$1, 2) is __________.