Question Number 6935 by FilupSmith last updated on 05/Aug/16 $$\boldsymbol{{v}}=<{x}_{{v}} ,\:{y}_{{v}} > \\ $$$$\boldsymbol{{u}}=<{x}_{{u}} ,\:{y}_{{u}} > \\ $$$$\boldsymbol{{v}}\:\mathrm{and}\:\boldsymbol{{u}}\:\mathrm{have}\:\mathrm{angles}: \\ $$$$\theta_{{v}} =\mathrm{tan}\left(\frac{{y}_{{v}} }{{x}_{{v}} }\right)\:\mathrm{and}\:\theta_{{u}} =\mathrm{tan}\left(\frac{{y}_{{u}} }{{x}_{{u}}…
Question Number 6923 by Tawakalitu. last updated on 03/Aug/16 $${Find}\:{the}\:{principal}\:{value}\:{of}\:\left(\mathrm{3}\:+\:\mathrm{4}{i}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Commented by Yozzii last updated on 03/Aug/16 $$\mathrm{3}+\mathrm{4}{i}=\sqrt{\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} }{e}^{{itan}^{−\mathrm{1}} \left(\mathrm{4}/\mathrm{3}\right)} =\mathrm{5}{e}^{{itan}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{3}}}…
Question Number 137970 by Dwaipayan Shikari last updated on 08/Apr/21 $${Prove}\:{that}\: \\ $$$$\bigtriangledown^{\mathrm{2}} \boldsymbol{\phi}=−\mathrm{4}\boldsymbol{\pi{G}}\rho\:\: \\ $$$$\phi={Potential}\:{of}\:{Gravitational}\:{field} \\ $$$$\rho={Density}\:\:\:\boldsymbol{{G}}={Universal}\:{Gravitational}\:{Constant} \\ $$ Answered by ajfour last updated…
Question Number 6875 by FilupSmith last updated on 01/Aug/16 $$\mathrm{For}\:\mathrm{vectors}\:\boldsymbol{{v}}\:\mathrm{and}\:\boldsymbol{{u}}\:\mathrm{where}: \\ $$$$\boldsymbol{{v}},\boldsymbol{{u}}\in\mathbb{R}^{{n}} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\boldsymbol{{v}}\:\mathrm{and}\:\boldsymbol{{u}}? \\ $$$$\left(\mathrm{both}\:\mathrm{are}\:\mathrm{from}\:\mathrm{origin}\right) \\ $$ Commented by prakash jain last updated on…
Question Number 6820 by Tawakalitu. last updated on 29/Jul/16 $${The}\:{position}\:{vector}\:{of}\:{the}\:{point}\:{P}\:\:{at}\:{time}\:{t}\:{is}\:{given}\:{by}\: \\ $$$$\left(\alpha{tant}\right){i}\:+\:\left(\alpha{sect}\right){k}\:{where}\:\alpha\:{is}\:{positive}\:{constant}\:{and} \\ $$$$\mathrm{0}\leqslant{t}\leqslant\frac{\Pi}{\mathrm{2}}.\:\:{Show}\:{that}\:{the}\:{velocity}\:{and}\:{acceleration}\:{of}\:{P}\:\:{when} \\ $$$${t}\:=\:\mathrm{0}\:{are}\:{at}\:{right}\:{angle}\:{to}\:{each}\:{other}.\:{If}\:{A}\:{is}\:{the}\:{point}\:{with}\: \\ $$$${position}\:{vector}\:\alpha{j},\:{obtain}\:{the}\:{vector}\:{equation}\:{for}\:{the}\:{straight}\: \\ $$$${line}\:{AP}\:{at}\:{time}\:{t}.\:\:{If}\:{the}\:{point}\:{Q}\:{divides}\:{AP}\:\:{internally}\:{in}\:{the} \\ $$$${ratio}\:\left({cost}\right)\::\:\left(\mathrm{1}\:−\:{cost}\right).\:{Show}\:{that}\:{the}\:{acceleration}\:{of}\:{the}\:{point} \\ $$$${Q}\:{is}\:{constant}\:{in}\:{magnitude}\:{and}\:{is}\:{always}\:{directed}\:{towards}\:{a}\: \\…
Question Number 6778 by Tawakalitu. last updated on 24/Jul/16 $${If}\:{two}\:{forces}\:{P}\:{and}\:{Q}\:{acting}\:{at}\:\mathrm{0}\:{are}\:{represented}\:{by}\:{line}\:{OA} \\ $$$${and}\:{OB}\:{with}\:\phi\:{being}\:{the}\:{angle}\:{between}\:{the}\:{two}\:{forces}\:. \\ $$$${find}\:{their}\:{resultant}\:{in}\:{R}\:{in}\:{terms}\:{of}\:{P} \\ $$ Commented by prakash jain last updated on 25/Jul/16 $$\mathrm{By}\:\mathrm{cosine}\:\mathrm{rule}…
Question Number 6458 by sanusihammed last updated on 27/Jun/16 $${Find}\:{the}\:{curl}\:{of}\:{A} \\ $$$${if}\:{A}\:=\:\mathrm{3}{n}^{\mathrm{2}} {yi}\:−\:{yz}^{\mathrm{2}} {j}\:−\:{nzk} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 71986 by rajesh4661kumar@gmail.com last updated on 23/Oct/19 Answered by mind is power last updated on 23/Oct/19 $$\mathrm{not}\:\mathrm{unique}\:\mathrm{angle} \\ $$$$\mathrm{XY}=\left\{\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\in\mathbb{R}^{\mathrm{3}} :\mathrm{z}=\mathrm{0}\right\} \\ $$$$\mathrm{angle}\:\mathrm{between}\:\mathrm{vecror}\:\mathrm{and}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{not}\:\mathrm{defind}\: \\…
Question Number 6374 by sanusihammed last updated on 25/Jun/16 $${Show}\:{that} \\ $$$$\overset{−} {{a}}\:×\:\left({b}\:×\:{c}\right)\:=\:\left(\overset{−} {{a}}\:.\:\overset{−} {{c}}\right)\overset{−} {{b}}\:\:−\:\:\left(\overset{−} {{a}}\:.\:\overset{−} {{b}}\right)\overset{−} {{c}} \\ $$ Commented by FilupSmith last…
Question Number 6321 by sanusihammed last updated on 23/Jun/16 $${Determine}\:\in\:{and}\:{N}\:{by}\:{using}\:{vector}\:{such}\:{that}\:{point}\:\left(−\mathrm{1},\mathrm{3},\mathrm{2}\right), \\ $$$$\left(−\mathrm{4},−\mathrm{2},−\mathrm{2}\right)\:{and}\:\left(\mathrm{5},\in,{N}\right)\:{lies}\:{on}\:{a}\:{straight}\:{line} \\ $$$$ \\ $$ Answered by nburiburu last updated on 23/Jun/16 $${let}'{s}\:{find}\:{the}\:{line}: \\…