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(A) Let the coordinates of the point be $P(x, y, z)$.The distance of point $P$ from the $xy$-plane is $|z|$.The distance of point $P$ from the $yz$-pl

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$x - y + z = 0$

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(A) Let the coordinates of the point be $P(x, y, z)$.The distance of point $P$ from the $xy$-plane is $|z|$.The distance of point $P$ from the $yz$-plane is $|x|$.The distance of point $P$ from the $zx$-plane is $|y|$.According to the problem,the sum of the distances from the $xy$-plane and the $yz$-plane is equal to the distance from the $zx$-plane:$|z| + |x| = |y|$.Assuming the point lies in the first octant where $x, y, z > 0$,we have $x + z = y$,which simplifies to $x - y + z = 0$.

Find the locus of a point such that the sum of its distances from the $xy$-plane and the $yz$-plane is equal to its distance from the $zx$-plane.

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