Question Number 16401 by sushmitak last updated on 21/Jun/17 $$\boldsymbol{{v}}=\mathrm{2}\boldsymbol{{i}}+\mathrm{2}\boldsymbol{{j}}+\mathrm{5}\boldsymbol{{k}} \\ $$$$\boldsymbol{{r}}=\boldsymbol{{i}}+\mathrm{9}\boldsymbol{{j}}−\mathrm{8}\boldsymbol{{k}} \\ $$$$\mathrm{Find}\:\boldsymbol{\omega} \\ $$$$\mathrm{I}\:\mathrm{can}\:\mathrm{do}\:\frac{\boldsymbol{{r}}×\boldsymbol{{v}}}{{r}^{\mathrm{2}} }=\boldsymbol{\omega} \\ $$$$\mathrm{and}\:\mathrm{i}\:\mathrm{get}\:\boldsymbol{\omega}=\:\frac{\mathrm{61}\boldsymbol{{i}}−\mathrm{21}\boldsymbol{{j}}−\mathrm{16}\boldsymbol{{k}}}{\mathrm{146}} \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{dont}\:\mathrm{get}\:\boldsymbol{{w}}×\boldsymbol{{r}}=\boldsymbol{{v}}. \\ $$$${why}? \\ $$…
Question Number 16363 by Tinkutara last updated on 21/Jun/17 $$\mathrm{A}\:\mathrm{car}\:\mathrm{drives}\:\mathrm{due}\:\mathrm{north}\:\mathrm{at}\:\mathrm{50}\:\mathrm{km}/\mathrm{hr}. \\ $$$$\mathrm{Wind}\:\mathrm{blows}\:\mathrm{due}\:\mathrm{North}-\mathrm{West}\:\mathrm{at}\:\mathrm{50}\sqrt{\mathrm{2}} \\ $$$$\mathrm{km}/\mathrm{hr}.\:\mathrm{In}\:\mathrm{what}\:\mathrm{direction},\:\mathrm{a}\:\mathrm{flag} \\ $$$$\mathrm{hoisted}\:\mathrm{on}\:\mathrm{the}\:\mathrm{roof}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{points}? \\ $$ Commented by ajfour last updated on 22/Jun/17…
Question Number 16294 by Tinkutara last updated on 20/Jun/17 $$\mathrm{Two}\:\mathrm{particles},\:\mathrm{1}\:\mathrm{and}\:\mathrm{2},\:\mathrm{move}\:\mathrm{with} \\ $$$$\mathrm{constant}\:\mathrm{velocities}\:\overset{\rightarrow} {{v}_{\mathrm{1}} }\:\mathrm{and}\:\overset{\rightarrow} {{v}_{\mathrm{2}} }.\:\mathrm{At}\:\mathrm{the} \\ $$$$\mathrm{initial}\:\mathrm{moment},\:\mathrm{their}\:\mathrm{position}\:\mathrm{vectors} \\ $$$$\mathrm{are}\:\mathrm{equal}\:\mathrm{to}\:\overset{\rightarrow} {{r}_{\mathrm{1}} }\:\mathrm{and}\:\overset{\rightarrow} {{r}_{\mathrm{2}} }.\:\mathrm{How}\:\mathrm{must}\:\mathrm{these} \\…
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Question Number 16153 by Tinkutara last updated on 18/Jun/17 $$\mathrm{Is}\:\mathrm{angular}\:\mathrm{displacement}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\mathrm{quantity}? \\ $$ Answered by ajfour last updated on 18/Jun/17 $${only}\:{as}\:{long}\:{as}\:{it}\:{is}\:{very}\:{small}. \\ $$ Commented…
Question Number 147195 by mnjuly1970 last updated on 18/Jul/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Li}_{\:\mathrm{2}} \left(\:\sqrt{{x}}\:\right){dx}\:=\:? \\ $$$$ \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 147162 by nadovic last updated on 18/Jul/21 Answered by liberty last updated on 18/Jul/21 $$\left(\mathrm{1}\right)\overset{\rightarrow} {{p}}=\frac{\mathrm{2}}{\mathrm{5}}\overset{\rightarrow} {{a}}+\frac{\mathrm{1}}{\mathrm{5}}\overset{\rightarrow} {{b}}+\frac{\mathrm{2}}{\mathrm{5}}\overset{\rightarrow} {{c}} \\ $$$$\left(\mathrm{2}\right)\overset{\rightarrow} {{p}}.\overset{\rightarrow} {{b}}=\overset{\rightarrow}…
Question Number 16055 by Tinkutara last updated on 17/Jun/17 $$\mathrm{Let}\:{A}',\:{B}'\:\mathrm{and}\:{C}'\:\mathrm{be}\:\mathrm{the}\:\mathrm{midpoints}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sides}\:{BC},\:{CA}\:\mathrm{and}\:{AB}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{triangle}\:{ABC}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\overset{\rightarrow} {{AA}'}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\overset{\rightarrow} {{AB}}\:+\:\overset{\rightarrow} {{AC}}\right) \\ $$ Answered by mrW1 last…
Question Number 81498 by jagoll last updated on 13/Feb/20 $$\mathrm{what}\:\mathrm{the}\:\mathrm{formula} \\ $$$$\bar {\mathrm{a}}\:×\:\left(\bar {\mathrm{b}}×\bar {\mathrm{c}}\right)\:? \\ $$ Answered by TANMAY PANACEA last updated on 13/Feb/20…
Question Number 81295 by jagoll last updated on 11/Feb/20 $${what}\:{is}\:{vector}\:{unit}\:{orthogonal} \\ $$$${to}\:\left(\mathrm{1},\mathrm{2},−\mathrm{2}\right)\:{and}\:{parallel}\:{to}\: \\ $$$${yz}−{plane}? \\ $$ Commented by john santu last updated on 11/Feb/20 $${say}\:{this}\:{vector}\:\bar…