1
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
Out of Syllabus
Let the mirror image of the point (1, 3, a) with respect to the plane $$\overrightarrow r .\left( {2\widehat i - \widehat j + \widehat k} \right) - b = 0$$ be ($$-$$3, 5, 2). Then, the value of | a + b | is equal to ____________.
2
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
Out of Syllabus
Let P be a plane containing the line $${{x - 1} \over 3} = {{y + 6} \over 4} = {{z + 5} \over 2}$$ and parallel to the line $${{x - 1} \over 4} = {{y - 2} \over { - 3}} = {{z + 5} \over 7}$$. If the point (1, $$-$$1, $$\alpha$$) lies on the plane P, then the value of |5$$\alpha$$| is equal to ____________.
3
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
Out of Syllabus
Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, $$-$$3, 1) and (2, 3, $$-$$5) at the right angles. If a, b, c, d are integers, then the
minimum value of (a2 + b2 + c2 + d2) is _________.
4
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
Out of Syllabus
The equation of the planes parallel to the plane x $$-$$ 2y + 2z $$-$$ 3 = 0 which are at unit distance from the point (1, 2, 3) is ax + by + cz + d = 0. If (b $$-$$ d) = k(c $$-$$ a), then the positive value of k is :