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Question Number 131733 by LYKA last updated on 07/Feb/21

$$\mathit{f}\mathit{i}\mathit{n}\mathit{d}\mathit{t}\mathit{h}\mathit{e}\mathit{m}\mathit{i}\mathit{n}\mathit{i}\mathit{m}\mathit{u}\mathit{m}\mathit{d}\mathit{i}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\mathit{c}\mathit{e}$$$$\mathit{b}\mathit{e}\mathit{t}\mathit{w}\mathit{e}\mathit{e}\mathit{n}\mathit{t}\mathit{h}\mathit{e}\mathit{p}\mathit{o}\mathit{i}\mathit{n}\mathit{t}(1,1,1)and$$$$\mathit{t}\mathit{h}\mathit{e}\mathit{p}\mathit{l}\mathit{a}\mathit{n}\mathit{e}\mathit{x}+2\mathit{y}+3\mathit{z}=6$$$$$$

Answered by physicstutes last updated on 07/Feb/21

$$d=\mid \frac{{ax}_1+{by}_1+{cz}_1-D}{\sqrt{a^2+b^2+c^2}}\mid$$$$\Rightarrow d=\mid \frac{\left(1\right)\left(1\right)+2\left(1\right)+3\left(1\right)-6}{\sqrt{1^2+2^2+3^2}}\mid =0$$$$\mathrm{since}\mathrm{the}\mathrm{point}\mathrm{in}\mathrm{question}(1,1,1)\mathrm{lies}\mathrm{on}\mathrm{the}\mathrm{plane}$$$$\mathrm{hence}\mathrm{it}\mathrm{has}\mathrm{a}\mathrm{minimum}\mathrm{distance}\mathrm{of}0\mathrm{units}\mathrm{from}\mathrm{the}$$$$\mathrm{given}\mathrm{plane}.$$

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