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Q. 12

Expert-verifiedFound in: Page 1095

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

What is the difference between the graphs of

$\mathrm{G}(x,y,z)=2\mathbf{i}-3\mathbf{j}+z\mathbf{k}and\mathrm{F}(x,y,z)=-2\mathbf{i}+3\mathbf{j}-z\mathbf{k}$

The difference between the graphs are $\mathrm{F}(\mathrm{x},\mathrm{y},z)=-\mathrm{G}(x\mathit{,}y,z);\mathrm{at}(0,0)$.

What is the difference between the graphs of

$\mathrm{G}(x,y,z)=2\mathbf{i}-3\mathbf{j}+z\mathbf{k}and\mathrm{F}(x,y,z)=-2\mathbf{i}+3\mathbf{j}-z\mathbf{k}$

$\mathrm{For}\mathrm{every}\mathrm{point}(\mathrm{x},\mathrm{y},\mathrm{z})\in {\mathrm{\mathbb{R}}}^{3}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{can}\mathrm{write}\mathrm{F}(x\mathit{,}y)\mathrm{as}\phantom{\rule{0ex}{0ex}}\mathrm{F}(x,y,z)=-2\mathbf{i}+3\mathbf{j}-z\mathbf{k}\phantom{\rule{0ex}{0ex}}\mathrm{F}(x,y,z)=-(2\mathbf{i}-3\mathbf{j}+z\mathbf{k}\mathbf{)}\phantom{\rule{0ex}{0ex}}\mathrm{As}\mathrm{we}\mathrm{know}\mathrm{G}(x\mathit{,}y,z)=2\mathbf{i}-3\mathbf{j}+z\mathbf{k}\phantom{\rule{0ex}{0ex}}\mathrm{So}\mathrm{we}\mathrm{can}\mathrm{write}\phantom{\rule{0ex}{0ex}}\mathrm{F}(\mathrm{x},\mathrm{y},z)=-\mathrm{G}(x\mathit{,}y,z)\phantom{\rule{0ex}{0ex}}\mathrm{Hence}\mathrm{F}(\mathrm{x},\mathrm{y},z)=-\mathrm{G}(x\mathit{,}y,z);\mathrm{at}(0,0)$

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