1
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 :
2
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Out of Syllabus
Let P be an arbitrary point having sum of the squares of the distances from the planes x + y + z = 0, lx $$-$$ nz = 0 and x $$-$$ 2y + z = 0, equal to 9. If the locus of the point P is x2 + y2 + z2 = 9, then the value of l $$-$$ n is equal to _________.
3
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
Out of Syllabus
If the equation of the plane passing through the line of intersection of the planes 2x $$-$$ 7y + 4z $$-$$ 3 = 0, 3x $$-$$ 5y + 4z + 11 = 0 and the point ($$-$$2, 1, 3) is ax + by + cz $$-$$ 7 = 0, then the value of 2a + b + c $$-$$ 7 is ____________.
4
JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
Out of Syllabus
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 _________.