Question Number 54422 by gunawan last updated on 03/Feb/19 $$\mathrm{The}\:\mathrm{median}\:{AD}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:{ABC} \\ $$$$\mathrm{is}\:\mathrm{bisected}\:\mathrm{at}\:{E},\:{BE}\:\mathrm{meets}\:{AC}\:\mathrm{in}\:{F}, \\ $$$$\mathrm{then}\:{AF}\::\:{AC}\:= \\ $$ Commented by ajfour last updated on 03/Feb/19 Commented by…
Question Number 54421 by gunawan last updated on 03/Feb/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{vector}\:\boldsymbol{\mathrm{c}},\:\boldsymbol{\mathrm{a}}={x}\boldsymbol{\mathrm{i}}+{y}\boldsymbol{\mathrm{j}}+{z}\boldsymbol{\mathrm{k}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{j}} \\ $$$$\mathrm{are}\:\mathrm{such}\:\mathrm{that}\:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{c}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}\:\mathrm{form}\:\mathrm{a}\:\mathrm{right} \\ $$$$\mathrm{handed}\:\mathrm{system},\:\mathrm{then}\:\boldsymbol{\mathrm{c}}\:\mathrm{is} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 04/Feb/19 $$\left.{p}\left.{ls}\:{carify}\:{i}\right)\left({a}\:,{b},{c}\:\right)\:\:\:{ii}\right)\left({a},{c},{b}\right)\:{which}\:{one}\:{form} \\…
Question Number 54419 by gunawan last updated on 03/Feb/19 $$\mathrm{If}\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{i}}+\boldsymbol{\mathrm{j}}−\boldsymbol{\mathrm{k}},\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{i}}−\boldsymbol{\mathrm{j}}+\boldsymbol{\mathrm{k}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{unit} \\ $$$$\mathrm{vector}\:\bot\:\mathrm{to}\:\mathrm{the}\:\mathrm{vector}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\mathrm{coplanar} \\ $$$$\mathrm{with}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}},\:\mathrm{then}\:\mathrm{a}\:\mathrm{unit}\:\mathrm{vector}\:\boldsymbol{\mathrm{d}}\:\bot\:\mathrm{to} \\ $$$$\mathrm{both}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19…
Question Number 54420 by gunawan last updated on 03/Feb/19 $$\mathrm{Let}\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{i}}+\boldsymbol{\mathrm{j}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}=\mathrm{2}\boldsymbol{\mathrm{i}}−\boldsymbol{\mathrm{k}},\:\mathrm{the}\:\mathrm{point}\:\mathrm{of} \\ $$$$\mathrm{intersection}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lines}\:\boldsymbol{\mathrm{r}}×\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{b}}×\boldsymbol{\mathrm{a}} \\ $$$$\mathrm{and}\:\boldsymbol{\mathrm{r}}×\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{a}}×\boldsymbol{\mathrm{b}}\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19 $${r}={ix}+{jy}+{kz} \\…
Question Number 54418 by gunawan last updated on 03/Feb/19 $$\mathrm{The}\:\mathrm{projection}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vector}\:\boldsymbol{\mathrm{a}}=\mathrm{4}\boldsymbol{\mathrm{i}}−\mathrm{3}\boldsymbol{\mathrm{j}}+\mathrm{2}\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{axis}\:\mathrm{making}\:\mathrm{equal}\:\mathrm{acute}\:\mathrm{angles} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{axes}\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19 $$\boldsymbol{{a}}=\mathrm{4}\boldsymbol{{i}}−\mathrm{3}\boldsymbol{{j}}+\mathrm{2}\boldsymbol{{k}}\:\:\:{so}\:\:\mid\boldsymbol{{a}}\mid=\sqrt{\mathrm{4}^{\mathrm{2}} +\left(−\mathrm{3}\right)^{\mathrm{2}}…
Question Number 54417 by gunawan last updated on 03/Feb/19 $$\mathrm{A}\:\mathrm{force}\:\mathrm{of}\:\mathrm{39}\:\mathrm{kg}\:\mathrm{weight}\:\mathrm{is}\:\mathrm{acting}\:\mathrm{at}\:\mathrm{a} \\ $$$$\mathrm{point}\:{P}\left(−\mathrm{4},\:\mathrm{2},\:\mathrm{5}\right)\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction}\: \\ $$$$\mathrm{12}\boldsymbol{\mathrm{i}}−\mathrm{4}\boldsymbol{\mathrm{j}}−\mathrm{3}\boldsymbol{\mathrm{k}}.\:\mathrm{The}\:\mathrm{moment}\:\mathrm{of}\:\mathrm{this}\:\mathrm{force} \\ $$$$\mathrm{about}\:\mathrm{a}\:\mathrm{line}\:\mathrm{through}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{having} \\ $$$$\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{2}\boldsymbol{\mathrm{i}}−\mathrm{2}\boldsymbol{\mathrm{j}}+\boldsymbol{\mathrm{k}}\:\mathrm{is} \\ $$ Terms of Service Privacy Policy…
Question Number 54378 by ngo last updated on 02/Feb/19 $$\underset{\pi/\mathrm{3}} {\overset{\mathrm{3}\pi/\mathrm{2}} {\int}}\:\:\left[\:\mathrm{2}\:\mathrm{cos}\:{x}\:\right]\:{dx}\:= \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19 Commented by tanmay.chaudhury50@gmail.com last…
Question Number 54377 by ngo last updated on 02/Feb/19 $$\underset{\pi/\mathrm{3}} {\overset{\mathrm{3}\pi/\mathrm{2}} {\int}}\:\:\left[\:\mathrm{2}\:\mathrm{cos}\:{x}\:\right]\:{dx}\:= \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 54219 by 951172235v last updated on 31/Jan/19 $$\mathrm{tan}^{\mathrm{6}} \:\frac{\pi}{\mathrm{9}}−\mathrm{33}\:\mathrm{tan}^{\mathrm{4}} \frac{\pi}{\mathrm{9}}+\mathrm{27tan}^{\mathrm{2}} \:\frac{\pi}{\mathrm{9}}\:=\: \\ $$ Answered by math1967 last updated on 31/Jan/19 $${let}\:\frac{\pi}{\mathrm{9}}=\theta\therefore{tan}\mathrm{3}\theta=\sqrt{\mathrm{3}\:} \\ $$$$\:\:\:\:\Rightarrow\frac{\mathrm{3}{tan}\theta−\mathrm{tan}\:^{\mathrm{3}}…
Question Number 54034 by qw last updated on 28/Jan/19 $$\mathrm{If}\:{f}\left({x}\right)={f}\left({a}+{b}−{x}\right),\:\mathrm{then}\:\underset{{a}} {\overset{{b}} {\int}}\:{x}\:{f}\left({x}\right)\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 28/Jan/19 $$\int_{{a}} ^{{b}}…