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Question Number 119160 by zakirullah last updated on 22/Oct/20

Commented by zakirullah last updated on 22/Oct/20

$$\mathbf{find}\mathbf{the}\mathbf{position}\mathbf{vecter}\mathbf{of}\mathbf{a}\mathit{p}\mathbf{oint}\mathbf{R}$$$$\mathit{w}\mathit{h}\mathit{i}\mathit{c}\mathit{h}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{s}\mathit{t}\mathit{h}\mathit{e}\mathit{l}\mathit{i}\mathit{n}\mathit{e}\mathit{j}\mathit{o}\mathit{i}\mathit{n}\mathit{i}\mathit{n}\mathit{g}$$$$\mathit{t}\mathit{h}\mathit{e}\mathit{p}\mathit{o}\mathit{i}\mathit{n}\mathit{t}\mathit{w}\mathit{h}\mathit{o}\mathit{s}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{p}\mathit{o}\mathit{s}\mathit{i}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$$$\mathit{v}\mathit{e}\mathit{c}\mathit{t}\mathit{e}\mathit{r}\mathit{s}\mathit{a}\mathit{r}\mathit{e}\mathit{P}(\mathit{i}+2\mathit{j}-\mathit{k}),\mathit{Q}(-\mathit{i}+\mathit{j}+\mathit{k})\mathit{i}\mathit{n}$$$$\mathit{t}\mathit{h}\mathit{e}\mathit{r}\mathit{a}\mathit{t}\mathit{i}\mathit{o}2:1\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{n}\mathit{a}\mathit{l}\mathit{y}\mathit{a}\mathit{n}\mathit{d}\mathit{e}\mathit{x}\mathit{t}\mathit{e}\mathit{r}\mathit{n}\mathit{a}\mathit{l}\mathit{y}$$

Commented by zakirullah last updated on 22/Oct/20

$$\mathit{P}\mathit{l}\mathit{e}\mathit{a}\mathit{s}\mathit{e}\mathit{h}\mathit{e}\mathit{l}\mathit{p}??\upuparrows$$

Commented by PRITHWISH SEN 2 last updated on 22/Oct/20

$$\mathrm{R}=(\frac{2\times (-1)+1}{3},\frac{2\times 1+1\times 2}{3},\frac{2\times 1+1\times (-1)}{3})$$$$\mathrm{R}=(-\frac{1}{3},\frac{4}{3},\frac{1}{3})$$$$\mathrm{the}\mathrm{position}\mathrm{vector}$$$$=-\frac{1}{3}\hat{\mathbf{i}}+\frac{4}{3}\hat{\mathbf{j}}+\frac{1}{3}\hat{\mathbf{k}}\left(\mathrm{for}\mathrm{internally}\right)$$

Commented by zakirullah last updated on 22/Oct/20

$$\mathit{s}\mathit{o}\mathit{r}\mathit{r}\mathit{y}\mathit{s}\mathit{i}\mathit{r}\mathit{i}\mathit{t}\mathit{h}\mathit{i}\mathit{n}\mathit{k}\mathit{t}\mathit{h}\mathit{i}\mathit{s}\mathit{m}\mathit{a}\mathit{t}\mathit{h}\mathit{o}\mathit{d}\mathit{i}\mathit{s}$$$$\mathit{v}\mathit{e}\mathit{r}\mathit{y}\mathit{h}\mathit{i}\mathit{g}\mathit{h}$$$$\mathit{p}\mathit{l}\mathit{e}\mathit{a}\mathit{s}\mathit{e}\mathit{c}\mathit{a}\mathit{n}\mathit{y}\mathit{o}\mathit{u}\mathit{e}\mathit{x}\mathit{p}\mathit{l}\mathit{a}\mathit{i}\mathit{n}\mathit{i}\mathit{t}\mathit{i}\mathit{n}\mathit{a}\mathit{n}\mathit{o}\mathit{t}\mathit{h}\mathit{e}\mathit{r}\mathit{w}\mathit{a}\mathit{y}?$$

Commented by PRITHWISH SEN 2 last updated on 22/Oct/20

$$\mathrm{think}\mathrm{P}\mathrm{and}\mathrm{Q}\mathrm{as}\mathrm{points}\mathrm{in}3\mathrm{D}$$$$\mathrm{then}\mathrm{P}=(1,2,-1)\mathrm{\&}\mathrm{Q}=(-1,1,1)$$$$\mathrm{and}\mathrm{find}\mathrm{R}\mathrm{as}\mathrm{internally}\mathrm{divides}\mathrm{PQ}\mathrm{in}\mathrm{the}$$$$\mathrm{ratio}2:1\mathrm{by}\mathrm{the}\mathrm{use}\mathrm{of}\mathrm{section}\mathrm{fomula}.$$$$\mathrm{then}\mathrm{just}\mathrm{put}\mathrm{it}\mathrm{with}\mathbf{i},\mathbf{j},\mathbf{k}.$$

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