The shortest distance of the point (1,2,3) from x2 + y2 = 0 is

Engineering

Mathematics

Equation of Straight Line in 3D

Distance from a Plane

Question

The shortest distance of the point (1,2,3) from x²+ y²= 0 is

$\sqrt{14}$

$\sqrt{5}$

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x²+ y²= 0

∴ (x,y) ≡ (0,0)

Let point be ≡ (0,0,z) $d \equiv \sqrt{{(1 - 0)}^{2} + {(2 - 0)}^{2} + {(z - 3)}^{2}} = \sqrt{1 + 4 + {(z - 3)}^{2}} \Rightarrow {(z - 3)}^{2} \geq 0$

d_{\min} = \sqrt{5}