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Category: Vector

Let-H-be-orthocenter-of-ABC-and-O-its-circumcenter-Prove-that-the-vectors-OA-OB-OC-and-OH-satisfy-the-following-equality-OA-OB-OC-OH-

Question Number 16748 by Tinkutara last updated on 26/Jun/17 $$\mathrm{Let}\:{H}\:\mathrm{be}\:\mathrm{orthocenter}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{and}\:{O} \\ $$$$\mathrm{its}\:\mathrm{circumcenter}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{vectors} \\ $$$$\overset{\rightarrow} {{OA}},\:\overset{\rightarrow} {{OB}},\:\overset{\rightarrow} {{OC}}\:\mathrm{and}\:\overset{\rightarrow} {{OH}}\:\mathrm{satisfy}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{equality}: \\ $$$$\overset{\rightarrow} {{OA}}\:+\:\overset{\rightarrow} {{OB}}\:+\:\overset{\rightarrow} {{OC}}\:=\:\overset{\rightarrow}…

A-particle-moves-with-a-speed-of-10-ms-1-from-the-point-2-2-in-the-direction-3i-4j-The-position-vector-after-3-s-is-

Question Number 16656 by Tinkutara last updated on 24/Jun/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{10} \\ $$$$\mathrm{ms}^{−\mathrm{1}} \:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\:−\mathrm{2}\right)\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{direction}\:\mathrm{3}\overset{\wedge} {{i}}\:+\:\mathrm{4}\overset{\wedge} {{j}}.\:\mathrm{The}\:\mathrm{position}\:\mathrm{vector} \\ $$$$\mathrm{after}\:\mathrm{3}\:\mathrm{s}\:\mathrm{is} \\ $$ Answered by sma3l2996 last…

g-M-2MB-MC-MC-MA-MA-MB-g-G-4MA-2-3MA-AB-AC-1-show-that-M-plan-g-M-g-G-4MG-2-2-Determine-the-set-of-point-M-of-plan-such-as-g-M-g-A-2-Construct-this-set-of-p

Question Number 82056 by mathocean1 last updated on 17/Feb/20 $${g}\left({M}\right)=\mathrm{2}{M}\overset{\rightarrow} {{B}}.{M}\overset{\rightarrow} {{C}}+{M}\overset{\rightarrow} {{C}}.{M}\overset{\rightarrow} {{A}}+{M}\overset{\rightarrow} {{A}}.{M}\overset{\rightarrow} {{B}} \\ $$$${g}\left({G}\right)=\mathrm{4}{MA}^{\mathrm{2}} +\mathrm{3}{M}\overset{\rightarrow} {{A}}\left({A}\overset{\rightarrow} {{B}}+{A}\overset{\rightarrow} {{C}}\right) \\ $$$$ \\…

The-acceleration-vector-of-a-particle-in-uniform-circular-motion-averaged-over-one-cycle-is-a-null-vector-True-False-

Question Number 16502 by Tinkutara last updated on 23/Jun/17 $$\mathrm{The}\:\mathrm{acceleration}\:\mathrm{vector}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{in} \\ $$$$\mathrm{uniform}\:\mathrm{circular}\:\mathrm{motion}\:\mathrm{averaged}\:\mathrm{over} \\ $$$$\mathrm{one}\:\mathrm{cycle}\:\mathrm{is}\:\mathrm{a}\:\mathrm{null}\:\mathrm{vector}.\:\left(\mathrm{True}/\mathrm{False}\right) \\ $$ Answered by ajfour last updated on 23/Jun/17 $$\bar {{a}}=\:−\frac{{v}_{\mathrm{0}}…

Rain-is-falling-vertically-with-a-speed-of-4-m-s-After-some-time-wind-starts-blowing-with-a-speed-of-3-m-s-in-the-north-to-south-direction-In-order-to-protect-himself-from-rain-a-man-standing-on-t

Question Number 16489 by Tinkutara last updated on 23/Jun/17 $$\mathrm{Rain}\:\mathrm{is}\:\mathrm{falling}\:\mathrm{vertically}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{4}\:\mathrm{m}/\mathrm{s}.\:\mathrm{After}\:\mathrm{some}\:\mathrm{time},\:\mathrm{wind}\:\mathrm{starts} \\ $$$$\mathrm{blowing}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{3}\:\mathrm{m}/\mathrm{s}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{north}\:\mathrm{to}\:\mathrm{south}\:\mathrm{direction}.\:\mathrm{In}\:\mathrm{order}\:\mathrm{to} \\ $$$$\mathrm{protect}\:\mathrm{himself}\:\mathrm{from}\:\mathrm{rain},\:\mathrm{a}\:\mathrm{man} \\ $$$$\mathrm{standing}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{should}\:\mathrm{hold}\:\mathrm{his} \\ $$$$\mathrm{umbrella}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{given}\:\mathrm{by} \\ $$$$\left(\mathrm{1}\right)\:\theta\:=\:\mathrm{tan}^{−\mathrm{1}} \mathrm{3}/\mathrm{4}\:\mathrm{with}\:\mathrm{the}\:\mathrm{vertical}…

v-2i-2j-5k-r-i-9j-8k-Find-I-can-do-r-v-r-2-and-i-get-61i-21j-16k-146-but-i-dont-get-w-r-v-why-

Question Number 16401 by sushmitak last updated on 21/Jun/17 $$\boldsymbol{{v}}=\mathrm{2}\boldsymbol{{i}}+\mathrm{2}\boldsymbol{{j}}+\mathrm{5}\boldsymbol{{k}} \\ $$$$\boldsymbol{{r}}=\boldsymbol{{i}}+\mathrm{9}\boldsymbol{{j}}−\mathrm{8}\boldsymbol{{k}} \\ $$$$\mathrm{Find}\:\boldsymbol{\omega} \\ $$$$\mathrm{I}\:\mathrm{can}\:\mathrm{do}\:\frac{\boldsymbol{{r}}×\boldsymbol{{v}}}{{r}^{\mathrm{2}} }=\boldsymbol{\omega} \\ $$$$\mathrm{and}\:\mathrm{i}\:\mathrm{get}\:\boldsymbol{\omega}=\:\frac{\mathrm{61}\boldsymbol{{i}}−\mathrm{21}\boldsymbol{{j}}−\mathrm{16}\boldsymbol{{k}}}{\mathrm{146}} \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{dont}\:\mathrm{get}\:\boldsymbol{{w}}×\boldsymbol{{r}}=\boldsymbol{{v}}. \\ $$$${why}? \\ $$…

A-car-drives-due-north-at-50-km-hr-Wind-blows-due-North-West-at-50-2-km-hr-In-what-direction-a-flag-hoisted-on-the-roof-of-the-car-points-

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…

Two-particles-1-and-2-move-with-constant-velocities-v-1-and-v-2-At-the-initial-moment-their-position-vectors-are-equal-to-r-1-and-r-2-How-must-these-four-vectors-be-interr

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} \\…