1
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
Out of Syllabus
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 _______.
2
JEE Main 2020 (Online) 9th January Evening Slot
Numerical
+4
-0
Out of Syllabus
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 ______.
3
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 ____________.
4
JEE Main 2020 (Online) 7th January Evening Slot
Numerical
+4
-0
If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through ($$\alpha$$, 7, 1) is $$\left( {{5 \over 3},{7 \over 3},{{17} \over 3}} \right)$$, then $$\alpha$$ is equal to______.