1
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
Out of Syllabus
The distance of the point P(3, 4, 4) from the point of intersection of the line joining the points. Q(3, $$-$$4, $$-$$5) and R(2, $$-$$3, 1) and the plane 2x + y + z = 7, is equal to ______________.
2
JEE Main 2021 (Online) 27th July Morning Shift
Numerical
+4
-1
Out of Syllabus
Let a plane P pass through the point (3, 7, $$-$$7) and contain the line, $${{x - 2} \over { - 3}} = {{y - 3} \over 2} = {{z + 2} \over 1}$$. If distance of the plane P from the origin is d, then d2 is equal to ______________.
3
JEE Main 2021 (Online) 25th July Evening Shift
Numerical
+4
-1
Out of Syllabus
If the lines $${{x - k} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$$ and
$${{x + 1} \over 3} = {{y + 2} \over 2} = {{z + 3} \over 1}$$ are co-planar, then the value of k is _____________.
4
JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
Out of Syllabus
Let P be a plane passing through the points (1, 0, 1), (1, $$-$$2, 1) and (0, 1, $$-$$2). Let a vector $$\overrightarrow a = \alpha \widehat i + \beta \widehat j + \gamma \widehat k$$ be such that $$\overrightarrow a$$ is parallel to the plane P, perpendicular to $$(\widehat i + 2\widehat j + 3\widehat k)$$ and $$\overrightarrow a \,.\,(\widehat i + \widehat j + 2\widehat k) = 2$$, then $${(\alpha - \beta + \gamma )^2}$$ equals ____________.