Question Number 27 by user1 last updated on 25/Jan/15 $$\mathrm{If}\:\boldsymbol{\mathrm{f}}={x}^{\mathrm{2}} {z}\boldsymbol{\mathrm{i}}−\mathrm{2}{y}^{\mathrm{3}} {z}^{\mathrm{2}} \boldsymbol{\mathrm{j}}+{xy}^{\mathrm{2}} {z}\boldsymbol{\mathrm{k}}.\:\mathrm{Find}\:{div}\:\boldsymbol{\mathrm{f}},\:{curl}\:\boldsymbol{\mathrm{f}},\: \\ $$$${at}\left(\mathrm{1},\:−\mathrm{1},\:\mathrm{1}\right). \\ $$ Answered by user1 last updated on 03/Nov/14…
Question Number 4 by user1 last updated on 25/Jan/15 $$\mathrm{If} \\ $$$$\mathrm{F}\left({y}\frac{\partial{f}}{\partial{z}}−{z}\frac{\partial{f}}{\partial{y}}\right)\boldsymbol{\mathrm{i}}+\left({z}\frac{\partial{f}}{\partial{x}}−{x}\frac{\partial{f}}{\partial{z}}\right)\boldsymbol{\mathrm{j}}+\left({x}\frac{\partial{f}}{\partial{y}}−{y}\frac{\partial{f}}{\partial{x}}\right)\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\:\:\boldsymbol{\mathrm{F}}=\boldsymbol{\mathrm{r}}×\bigtriangledown{f}. \\ $$ Answered by user1 last updated on 29/Oct/14 $$\:\:\boldsymbol{\mathrm{r}}×\bigtriangledown\boldsymbol{\mathrm{f}}=\begin{vmatrix}{\boldsymbol{\mathrm{i}}}&{\boldsymbol{\mathrm{j}}}&{\boldsymbol{\mathrm{k}}}\\{{x}}&{{y}}&{{z}}\\{\frac{\partial{f}}{\partial{x}}}&{\frac{\partial{f}}{\partial{y}}}&{\frac{\partial{f}}{\partial{z}}}\end{vmatrix} \\…
Question Number 2 by user1 last updated on 25/Jan/15 $$\mathrm{Find}\:\mathrm{grad}\:{log}\:\mid\boldsymbol{\mathrm{r}}\mid. \\ $$ Answered by user1 last updated on 29/Oct/14 $$\mathrm{We}\:\mathrm{have}\:\:\:{r}=\sqrt{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)} \\ $$$$\mathrm{log}\:\mid\boldsymbol{\mathrm{r}}\mid=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\left({x}^{\mathrm{2}}…
Question Number 78522 by jagoll last updated on 18/Jan/20 $${what}\:{is}\:{the}\: \\ $$$${line}\:{passing}\:{through}\:\left(\mathrm{2},\mathrm{2},\mathrm{1}\right) \\ $$$${and}\:{parallel}\:{to}\:\mathrm{2}\hat {{i}}\:−\:\hat {{j}}\:−\:\hat {{k}}\:? \\ $$ Commented by mr W last updated…
Question Number 76302 by john santuy last updated on 26/Dec/19 $${given}\:{vektor}\:{a}=\left(\mathrm{3},{x},−\mathrm{2}\right) \\ $$$${b}=\left(−\mathrm{6},−\mathrm{2},{y}\right)\:.\:{what}\:{the}\:{value}\:{x}\: \\ $$$${and}\:{y}\:{if}\:{a}\:{and}\:{b}\:{are}\:{parallel}? \\ $$ Answered by benjo last updated on 26/Dec/19 $$\mathrm{a}×\mathrm{b}\:=\mathrm{0}…
Question Number 9604 by madscientist last updated on 20/Dec/16 $${is}\: \\ $$$$\bigtriangledown×\left(\bigtriangledown×{A}\right)=\bigtriangledown\left(\bigtriangledown\centerdot{A}\right)−\bigtriangledown^{\mathrm{2}} {A} \\ $$$${F}×\left(\bigtriangledown×{A}\right)={F}\left(\bigtriangledown\centerdot{A}\right)−\bigtriangledown^{\mathrm{2}} {A} \\ $$$${the}\:{same}? \\ $$ Terms of Service Privacy Policy…
Question Number 75101 by Rio Michael last updated on 07/Dec/19 $${the}\:{vector}\:{equations}\:{of}\:{two}\:{lines}\:{L}_{\mathrm{1}} \:{and}\:{L}_{\mathrm{2}} \:{is}\:{given}\:{by} \\ $$$$\:{L}_{\mathrm{1}} :{r}=\:\boldsymbol{{i}}−\boldsymbol{{j}}+\mathrm{3}\boldsymbol{{k}}\:+\:\lambda\left(\boldsymbol{{i}}−\boldsymbol{{j}}\:+\boldsymbol{{k}}\right) \\ $$$${L}_{\mathrm{2}} \::\:{r}=\:\mathrm{2}\boldsymbol{{i}}+{a}\boldsymbol{{j}}\:+\:\mathrm{6}\boldsymbol{{k}}\:+\:\mu\left(\mathrm{2}\boldsymbol{{i}}\:+\:\boldsymbol{{j}}\:+\:\mathrm{3}\boldsymbol{{k}}\right) \\ $$$${where}\:{a},\lambda,\mu\:{are}\:{real}\:{constants}. \\ $$$${given}\:{that}\:{L}_{\mathrm{1}} \:{and}\:{L}_{\mathrm{2}} \:{intersect}\:{find}…
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Question Number 137559 by liberty last updated on 04/Apr/21 $$ \\ $$What is the volume of tetrahedron ABCD, whose vertices have the coordinates A (2,…