The coordinates of the points $A$ and $B$ are $(2, 3, 4)$ and $(-2, 5, -4)$ respectively. If a point $P(x, y, z)$ moves such that $PA^2 - PB^2 = k$,where $k$ is a constant,then the locus of $P$ is:

Let the plane $ax + by + cz = d$ pass through $(2, 3, -5)$ and be perpendicular to the planes $2x + y - 5z = 10$ and $3x + 5y - 7z = 12$. If $a, b, c, d$ are integers,$d > 0$,and $\text{gcd}(|a|, |b|, |c|, d) = 1$,then the value of $a + 7b + c + 20d$ is equal to

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x - y + 5z - 3 = 0$ are $ . . . . . . $.

If the planes $2x + 3y + 4z + 7 = 0$ and $4x + ky + 8z + 1 = 0$ are parallel,then the equation of the plane passing through the point $(k, k, k)$ and having the direction ratios of its normal as $(k-1, k, k+1)$ is

If the plane $56x + 4y + 9z = 2016$ meets the coordinate axes at points $A, B$,and $C$,then the centroid of the $\triangle ABC$ is

The equation of a plane containing the point $(1, -1, 1)$ and parallel to the plane $2x + 3y - 4z = 17$ is