The nearest point from the origin is

Engineering

Mathematics

Distance Formulae and Its Application

theorem in space

Distance from a Plane

Question

The nearest point from the origin is

(2,2,2)

(1,2,−1)

(−3,2,1)

(2,3,−1)

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Distance from the origin $= \sqrt{x^{2} + y^{2} + z^{2}}$

Distance from (2,3,–1) is

\sqrt{2^{2} + 3^{2} + {(- 1)}^{2}} = \sqrt{4 + 9 + 1} = \sqrt{14}

Distance from (–3,2,1) is

\sqrt{{(- 3)}^{2} + 2^{2} + 1^{2}} = \sqrt{9 + 4 + 1} = \sqrt{14}

Distance from (2,2,2) is

\sqrt{2^{2} + 2^{2} + 2^{2}} = \sqrt{8}

Distance from (1,2,–1) is

\sqrt{1^{2} + 2^{2} + {(- 1)}^{2}} = \sqrt{1 + 4 + 1} = \sqrt{6}

\sqrt{6}; \sqrt{8}; \sqrt{14}

Thus (1,2,–1) is nearest point from the origin.