1
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
A line 'l' passing through origin is perpendicular to the lines

$${l_1}:\overrightarrow r = (3 + t)\widehat i + ( - 1 + 2t)\widehat j + (4 + 2t)\widehat k$$

$${l_2}:\overrightarrow r = (3 + 2s)\widehat i + (3 + 2s)\widehat j + (2 + s)\widehat k$$

If the co-ordinates of the point in the first octant on 'l2‘ at a distance of $$\sqrt {17}$$ from the point of intersection of 'l' and 'l1' are (a, b, c) then 18(a + b + c) is equal to ___________.
2
JEE Main 2021 (Online) 24th February Evening Shift
Numerical
+4
-1
Let $$\lambda$$ be an integer. If the shortest distance between the lines

x $$-$$ $$\lambda$$ = 2y $$-$$ 1 = $$-$$2z and x = y + 2$$\lambda$$ = z $$-$$ $$\lambda$$ is $${{\sqrt 7 } \over {2\sqrt 2 }}$$, then the value of | $$\lambda$$ | is _________.
3
JEE Main 2020 (Online) 4th September Morning Slot
Numerical
+4
-0
If the equation of a plane P, passing through the intersection of the planes,
x + 4y - z + 7 = 0 and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b $$\in$$ R, then the distance of the point (3, 2, -1) from the plane P is...........
4
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
Let a plane P contain two lines
$$\overrightarrow r = \widehat i + \lambda \left( {\widehat i + \widehat j} \right)$$, $$\lambda \in R$$ and
$$\overrightarrow r = - \widehat j + \mu \left( {\widehat j - \widehat k} \right)$$, $$\mu \in R$$
If Q($$\alpha$$, $$\beta$$, $$\gamma$$) is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then 3($$\alpha$$ + $$\beta$$ + $$\gamma$$) equals _______.
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