A point moves so that its distances from the points $(3, 4, - 2)$ and $(2, 3, - 3)$ remains equal. The locus of the point is

A line

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A plane whose normal is equally inclined to axes

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A sphere

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None of these

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Solution

The correct option is A A line
Let the pt $(x, y, z)$
$(x - 3)^{2} + (y - 4)^{2} + (z + 2)^{2} = (x - 2)^{2} + (y - 3)^{2} + (z + 3)^{2}$
$x^{2} + 9 - 6 x + y^{2} - 3 y + 16 + z^{2} + 4 z + 4 = x^{2} + 4 - 2 z + y^{2} - 6 x + 9 + z^{2} + 6 z + 9$
$4 z + 2 y + 2 z = 7$ a line

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A point moves so that its distances from the points (3,4,−2) and (2,3,−3) remains equal. The locus of the point is

The correct option is A A lineLet the pt (x,y,z)(x−3)2+(y−4)2+(z+2)2=(x−2)2+(y−3)2+(z+3)2x2+9−6x+y2−3y+16+z2+4z+4=x2+4−2z+y2−6x+9+z2+6z+94z+2y+2z=7 a line

A point moves so that its distances from the points $(3, 4, - 2)$ and $(2, 3, - 3)$ remains equal. The locus of the point is

The correct option is A A line
Let the pt $(x, y, z)$
$(x - 3)^{2} + (y - 4)^{2} + (z + 2)^{2} = (x - 2)^{2} + (y - 3)^{2} + (z + 3)^{2}$
$x^{2} + 9 - 6 x + y^{2} - 3 y + 16 + z^{2} + 4 z + 4 = x^{2} + 4 - 2 z + y^{2} - 6 x + 9 + z^{2} + 6 z + 9$
$4 z + 2 y + 2 z = 7$ a line