Question Number 205321 by gopikrishnan last updated on 16/Mar/24 $$\overset{\rightarrow} {{a}}=\hat {{i}}+\mathrm{3}\hat {{j}}+\mathrm{4}\hat {{k}}\:\overset{\rightarrow} {{b}}=\mathrm{2}\hat {{i}}−\mathrm{3}\hat {{j}}+\mathrm{4}\hat {{k}}\:\overset{\rightarrow} {{c}}=\mathrm{5}\hat {{i}}−\mathrm{2}\hat {{j}}+\mathrm{4}\hat {{k}}\:{given}\:{that}\:\overset{\rightarrow} {{p}}×\overset{\rightarrow} {{b}}=\overset{\rightarrow} {{b}}×\overset{\rightarrow}…
Question Number 205164 by depressiveshrek last updated on 11/Mar/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{1}−{x}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}−{x}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}−{x}}&{\ldots}&{{n}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}−{x}}\end{vmatrix} \\ $$ Answered by aleks041103 last updated on 12/Mar/24 $${By}\:{subtracting}\:{the}\:{first}\:{row}\:{from}\:{all}\:{other} \\ $$$$\begin{vmatrix}{\mathrm{1}−{x}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}−{x}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}−{x}}&{\ldots}&{{n}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}−{x}}\end{vmatrix}= \\…
Question Number 205156 by depressiveshrek last updated on 11/Mar/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{5}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{2}}&{\mathrm{5}}&{\mathrm{3}}&{\mathrm{0}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{2}}&{\mathrm{5}}&{\mathrm{3}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}&{\vdots}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{5}}&{\mathrm{3}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{2}}&{\mathrm{5}}\end{vmatrix} \\ $$ Answered by pi314 last updated on 11/Mar/24 $$\Delta_{{n}} =\begin{vmatrix}{\mathrm{5}\:\mathrm{3}\:\:\:\mathrm{0}\:\mathrm{0}……\mathrm{0}\:\mathrm{0}}\\{\mathrm{2}\:\:\mathrm{5}\:\:\mathrm{3}\:\mathrm{0}……\mathrm{0}\:\mathrm{0}}\\{\mathrm{0}\:\:\mathrm{2}\:\:\mathrm{5}\:\mathrm{3}……\mathrm{0}\:\:\mathrm{0}}\\{………………\mathrm{5}\:\mathrm{3}}\\{\mathrm{0}\:\mathrm{0}\:\mathrm{0}\:\:\mathrm{0}…….\:\mathrm{2}\:\mathrm{5}}\end{vmatrix} \\ $$$$\Delta_{{n}}…
Question Number 204509 by JohnSmith last updated on 19/Feb/24 Commented by Rasheed.Sindhi last updated on 20/Feb/24 $$\mathcal{N}{ot}\:{clear}! \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 203419 by essaad last updated on 18/Jan/24 Commented by mr W last updated on 18/Jan/24 $${question}\:{is}\:{wrong}!\:{you}\:{can}\:{not} \\ $$$${determine}\:\alpha\:{uniquely}. \\ $$ Commented by essaad…
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Question Number 201526 by 281981 last updated on 08/Dec/23 Answered by AST last updated on 08/Dec/23 $${WLOG},{let}\:{O}\:{be}\:{the}\:{origin};\:{g}=\frac{{a}+{b}+{c}}{\mathrm{3}} \\ $$$$\mid{o}−{a}\mid=\mid{o}−{b}\mid=\mid{o}−{c}\mid={R} \\ $$$$\Rightarrow\left({o}−{a}\right)\left(\overset{−} {{o}}−\overset{−} {{a}}\right)={R}^{\mathrm{2}} \Rightarrow{a}\overset{−} {{a}}={R}^{\mathrm{2}}…
Question Number 201135 by 281981 last updated on 30/Nov/23 Answered by MM42 last updated on 30/Nov/23 $${SX}+{SM}=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}{SM}=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\left({SP}+{PQ}+{QM}\right)=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\left(\frac{\mathrm{4}{a}−{b}}{\mathrm{2}}\right)=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\Rightarrow{m}+{n}=\frac{\mathrm{9}}{\mathrm{10}}\:\:\checkmark\:\:\left(\mathrm{1}\right)…
Question Number 201107 by behi834171 last updated on 29/Nov/23 $${two}\:{weels},\:{those}\:{have}\:{the}\:{same}\:{materials}, \\ $$$${with}\:{radii}:\boldsymbol{{r}}_{\mathrm{1}} =\mathrm{4}\:{and}\:\boldsymbol{{r}}_{\mathrm{2}} =\mathrm{14} \\ $$$${are}\:{starting}\:{to}\:{move}\:{on}\:{a}\:{surface},{with} \\ $$$${the}\:{same}\:{velocity},{from}:\boldsymbol{{x}}=\mathrm{0}\:{to}\:\boldsymbol{{x}}=\mathrm{20}. \\ $$$${the}\:{surface}\:{has}\:{no}\:{friction}. \\ $$$${wich}\:{one}\:{arrives}\:{faster}? \\ $$$${any}\:{informations}\:{needed}? \\…
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