The nearest point from the origin is

Engineering

Mathematics

Line of Greatest Slope

Question

(2, 3, - 1)

(- 3, 2, 1)

(2, 2, 2)

(1, 2, - 1)

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Distance from the origin

= \sqrt{x^{2} + y^{2} + z^{2}}

Distance from

(2, 3, - 1)

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

Distance from

(- 3, 2, 1)

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

Distance from

(2, 2, 2)

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

Distance from

(1, 2, - 1)

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

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

Thus

(1, 2, - 1)

is nearest point from the origin.

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