Question Number 13942 by FilupS last updated on 25/May/17 $$\mathrm{for}\:\:\boldsymbol{{v}}=\begin{bmatrix}{{y}}\\{{x}}\end{bmatrix},\:\:\:\:\boldsymbol{{v}}\in\mathbb{R}^{\mathrm{2}} \\ $$$$\boldsymbol{{v}}\:\mathrm{has}\:\mathrm{basis}\:\mathrm{vectors}\:\hat {{i}}\:\mathrm{and}\:\hat {{j}} \\ $$$$\: \\ $$$$\mathrm{Assume}\:\mathrm{we}\:\mathrm{apply}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{transform}\:\mathrm{to} \\ $$$$\mathrm{obtain}\:\mathrm{new}\:\mathrm{basis}\:\mathrm{vectors}\:\hat {{i}}'\:\mathrm{and}\:\hat {{j}}' \\ $$$$\: \\…
Question Number 79308 by M±th+et£s last updated on 24/Jan/20 Commented by mr W last updated on 24/Jan/20 $${does}\:{this}\:{help}: \\ $$ Commented by mr W last…
Question Number 79131 by mathocean1 last updated on 23/Jan/20 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:\mathrm{M}\: \\ $$$$\mathrm{such}\:\mathrm{as}\:\mid\mid\mathrm{M}\overset{\rightarrow} {\mathrm{A}}+\mathrm{M}\overset{\rightarrow} {\mathrm{B}}+\mathrm{2M}\overset{\rightarrow} {\mathrm{C}}\mid\mid=\mathrm{6}\sqrt{\mathrm{3}} \\ $$$$\mathrm{AB}=\mathrm{BC}=\mathrm{AC}=\mathrm{6} \\ $$$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{triangle}. \\ $$ Commented by mathocean1 last…
Question Number 79121 by M±th+et£s last updated on 22/Jan/20 Answered by mr W last updated on 23/Jan/20 Commented by mr W last updated on 23/Jan/20…
Question Number 144166 by liberty last updated on 22/Jun/21 $$\mathrm{Given}\:\overset{\rightarrow} {\mathrm{p}}=\sqrt{\mathrm{2}}\:\hat {\mathrm{i}}+\mathrm{2}\sqrt{\mathrm{3}}\:\hat {\mathrm{j}}+\:\sqrt{\mathrm{3}}\:\hat {\mathrm{k}}\:\&\: \\ $$$$\:\overset{\rightarrow} {\mathrm{q}}=\mathrm{a}\:\hat {\mathrm{i}}+\hat {\mathrm{j}}\:+\mathrm{2}\hat {\mathrm{k}}\:.\:\mathrm{If}\:\mathrm{proj}_{\overset{\rightarrow} {\mathrm{q}}} \:\overset{\rightarrow} {\mathrm{p}}\:=\:\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{9}}\:\overset{\rightarrow} {\mathrm{q}}\: \\…
Question Number 337 by Vishal Bhardwaj last updated on 25/Jan/15 $$\int\left(\sqrt{{cotx}}+\sqrt{{tanx}}\right)\:{dx} \\ $$ Answered by prakash jain last updated on 22/Dec/14 $$\int\sqrt{\mathrm{cot}\:{x}}{dx}+\int\sqrt{\mathrm{tan}\:{x}}{dx} \\ $$$$\mathrm{Please}\:\mathrm{see}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{Q119}\:\mathrm{for}\:\mathrm{integration} \\…
Question Number 225 by 123456 last updated on 25/Jan/15 $$\boldsymbol{\mathrm{u}}=\mathrm{2}\boldsymbol{\mathrm{i}}+\mathrm{3}\boldsymbol{\mathrm{j}}+\mathrm{5}\boldsymbol{\mathrm{k}} \\ $$$$\boldsymbol{\mathrm{v}}=\mathrm{3}\boldsymbol{\mathrm{i}}+\mathrm{2}\boldsymbol{\mathrm{j}}−\mathrm{5}\boldsymbol{\mathrm{k}} \\ $$$$\boldsymbol{\mathrm{w}}=−\mathrm{2}\boldsymbol{\mathrm{i}}+\mathrm{3}\boldsymbol{\mathrm{j}}+\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{find} \\ $$$$\boldsymbol{\mathrm{u}}\centerdot\left(\boldsymbol{\mathrm{v}}×\boldsymbol{\mathrm{w}}\right)+\left(\boldsymbol{\mathrm{u}}×\boldsymbol{\mathrm{v}}\right)\centerdot\left(\boldsymbol{\mathrm{u}}×\boldsymbol{\mathrm{w}}\right) \\ $$ Answered by mreddy last updated…
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Question Number 78458 by kaivan.ahmadi last updated on 17/Jan/20 $${if}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {tan}^{{n}} {xdx}\:{and}\:{I}_{{n}} ={a}_{{n}} +{b}_{{n}} {I}_{{n}−\mathrm{2}} \:{then}\:{find}\:{a}_{\mathrm{10}} \\ $$ Commented by kaivan.ahmadi last updated…
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