Question

Find the points on z-axis which are at a distance √21 from the point (1, 2, 3).​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that the point on z - axis be P (0, 0, z).

Let assume that the point (1, 2, 3) be represented as A.

According to statement,

$\rm :\longmapsto\:AP = \sqrt{21}$

$\rm :\longmapsto\: {AP}^{2} = 21$

$\rm :\longmapsto\: {(0 - 1)}^{2} + {(0 - 2)}^{2} + {(z - 3)}^{2} = 21$

$\rm :\longmapsto\: 1 + 4+ {(z - 3)}^{2} = 21$

$\rm :\longmapsto\: 5+ {(z - 3)}^{2} = 21$

$\rm :\longmapsto\: {(z - 3)}^{2} = 21 - 5$

$\rm :\longmapsto\: {(z - 3)}^{2} = 16$

$\rm :\longmapsto\: {(z - 3)}^{2} = {4}^{2}$

$\rm :\longmapsto\:z - 3 \: = \: \pm \: 4$

Therefore, the point on z - axis be (0, 0, 4) and (0, 0, - 4).

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Distance Formula :-

Distance between two points A and B is given by

$\sf \:AB = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} + {(z_2-z_1)}^{2} }$