1

JEE Main 2021 (Online) 18th March Morning Shift

Numerical

+4

-1

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 (a

minimum value of (a

^{2}+ b^{2}+ c^{2}+ d^{2}) isYour input ____

2

JEE Main 2021 (Online) 18th March Morning Shift

Numerical

+4

-1

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

Your input ____

3

JEE Main 2021 (Online) 17th March Evening Shift

Numerical

+4

-1

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 x

^{2}+ y^{2}+ z^{2}= 9, then the value of l $$-$$ n is equal to _________.Your input ____

4

JEE Main 2021 (Online) 17th March Morning Shift

Numerical

+4

-1

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 ____________.

Your input ____

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