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)

Vedclass · Accepted Answer

$x - y + z = 0$

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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 $x - y + z = 0$.

Column $I$	Column $II$
$(A)$ The centroid of the triangle formed by $(2, 3, -1)$,$(5, 6, 3)$,$(2, -3, 1)$ is	$(p)$ $(2, 2, 2)$
$(B)$ The circumcentre of the triangle formed by $(1, 2, 3)$,$(2, 3, 1)$,$(3, 1, 2)$ is	$(q)$ $(3, 1, 4)$
$(C)$ The orthocentre of the triangle formed by $(2, 1, 5)$,$(3, 2, 3)$,$(4, 0, 4)$ is	$(r)$ $(1, 1, 0)$
$(D)$ The incentre of the triangle formed by $(0, 0, 0)$,$(3, 0, 0)$,$(0, 4, 0)$ is	$(s)$ $(3, 2, 1)$

$A$ 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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