A point moves in such a way that the sum of i | vedclass

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

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$x - y + z = 0$

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

$A$ point moves in such a way that the sum of its distances from the $xy$-plane and $yz$-plane remains equal to its distance from the $zx$-plane. The locus of the point is:

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