1
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...........
2
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 _______.
3
JEE Main 2020 (Online) 9th January Evening Slot
Numerical
+4
-0
If the distance between the plane, 23x – 10y – 2z + 48 = 0 and the plane

containing the lines $${{x + 1} \over 2} = {{y - 3} \over 4} = {{z + 1} \over 3}$$

and $${{x + 3} \over 2} = {{y + 2} \over 6} = {{z - 1} \over \lambda }\left( {\lambda \in R} \right)$$

is equal to $${k \over {\sqrt {633} }}$$, then k is equal to ______.
4
JEE Main 2020 (Online) 9th January Morning Slot
Numerical
+4
-0
The projection of the line segment joining the points (1, –1, 3) and (2, –4, 11) on the line joining the points (–1, 2, 3) and (3, –2, 10) is ____.
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