Category: Vector

Question Number 16917 by tawa tawa last updated on 28/Jun/17 $$\mathrm{If}\mathrm{x}+\mathrm{iy}=\frac{1}{\mathrm{a}+\mathrm{ib}}$$$$\mathrm{prove}\mathrm{that}:({\mathrm{x}}^2+{\mathrm{y}}^2)({\mathrm{a}}^2+{\mathrm{b}}^2)=1$$ Answered by Tinkutara last updated on…

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

Question Number 82277 by M±th+et£s last updated on 19/Feb/20 Commented by M±th+et£s last updated on 19/Feb/20 $$findtheareaoftherectangle$$ Commented by mr W last updated…

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

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