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JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
If the distance of the point (1, $$-$$2, 3) from the plane x + 2y $$-$$ 3z + 10 = 0 measured parallel to the line, $${{x - 1} \over 3} = {{2 - y} \over m} = {{z + 3} \over 1}$$ is $$\sqrt {{7 \over 2}}$$, then the value of |m| is equal to _________.
2
JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
Let $$\overrightarrow c$$ be a vector perpendicular to the vectors, $$\overrightarrow a$$ = $$\widehat i$$ + $$\widehat j$$ $$-$$ $$\widehat k$$ and
$$\overrightarrow b$$ = $$\widehat i$$ + 2$$\widehat j$$ + $$\widehat k$$. If $$\overrightarrow c \,.\,\left( {\widehat i + \widehat j + 3\widehat k} \right)$$ = 8 then the value of
$$\overrightarrow c$$ . $$\left( {\overrightarrow a \times \overrightarrow b } \right)$$ is equal to __________.
3
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
Let ($$\lambda$$, 2, 1) be a point on the plane which passes through the point (4, $$-$$2, 2). If the plane is perpendicular to the line joining the points ($$-$$2, $$-$$21, 29) and ($$-$$1, $$-$$16, 23), then $${\left( {{\lambda \over {11}}} \right)^2} - {{4\lambda } \over {11}} - 4$$ is equal to __________.
4
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 ___________.