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Q. What is the shortest distance of the point (1, 2, 3) from x- axis ?

Introduction to Three Dimensional Geometry

Solution:

Any point on x-axis has y = z = 0
Distance of the point (1, 2, 3) from x-axis is the distance between point (1, 2, 3) and point (1, 0, 0)
$=\sqrt{\left(1-1\right)^{2} + \left(2-0\right)^{2} +\left(3-0\right)^{2}} = \sqrt{2^{2} + 3^{2}}$
$ = \sqrt{4+9} = \sqrt{13}$