Question Number 130523 by benjo_mathlover last updated on 26/Jan/21 Answered by TheSupreme last updated on 26/Jan/21 $${P}\left(\mathrm{4},\mathrm{6},\mathrm{2}\right) \\ $$$$\begin{cases}{\mathrm{2}{x}−\mathrm{3}{y}=\mathrm{2}}\\{\mathrm{7}{x}−\mathrm{3}{z}=\mathrm{10}}\\{{x}+{y}−{z}=\mathrm{8}}\end{cases} \\ $$$$\begin{bmatrix}{\mathrm{2}}&{−\mathrm{3}}&{\mathrm{0}}\\{\mathrm{7}}&{\mathrm{0}}&{−\mathrm{3}}\\{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix}\begin{pmatrix}{{x}}\\{{y}}\\{{z}}\end{pmatrix}=\begin{pmatrix}{\mathrm{2}}\\{\mathrm{10}}\\{\mathrm{8}}\end{pmatrix} \\ $$$${n}_{\mathrm{1}} −{n}_{\mathrm{2}} +\mathrm{3}{n}_{\mathrm{3}}…
Question Number 64348 by Rio Michael last updated on 16/Jul/19 $${the}\:{vectors}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}\:{are}\:{such}\:{that}\:\mid\boldsymbol{{a}}\mid\:=\mathrm{3}\:,\:\mid\boldsymbol{{b}}\mid=\mathrm{5}\:{and}\:\boldsymbol{{a}}.\boldsymbol{{b}}=−\mathrm{14} \\ $$$${find}\:\mid\boldsymbol{{a}}−\boldsymbol{{b}}\mid \\ $$ Answered by Tanmay chaudhury last updated on 17/Jul/19 $$\mid\boldsymbol{{a}}−\boldsymbol{{b}}\mid^{\mathrm{2}} =\left(\boldsymbol{{a}}−\boldsymbol{{b}}\right).\left(\boldsymbol{{a}}−\boldsymbol{{b}}\right)…
Question Number 129804 by bramlexs22 last updated on 19/Jan/21 $$\mathrm{If}\:\overset{\rightarrow} {{p}}=\mathrm{2}\hat {{i}}+\mathrm{5}\hat {{j}}+\mathrm{6}\hat {{k}} \\ $$$$\:\:\:\overset{\rightarrow} {{q}}=\mathrm{3}\hat {{i}}+\mathrm{6}\hat {{j}}+\mathrm{8}\hat {{k}} \\ $$$$\:\:\:\overset{\rightarrow} {{r}}=\mathrm{2}\hat {{i}}+\mathrm{6}\hat {{j}}+\mathrm{10}\hat…
Question Number 64085 by Rio Michael last updated on 12/Jul/19 $${please}\:{just}\:{read}\:{equation}\:{of}\:{a}\:{line}\:{and}\:{a}\:{plane}\:{in}\:{vectors}. \\ $$$${i}\:{don}'{t}\:{understand}\: \\ $$$$\:\:\left(\boldsymbol{{r}}−\boldsymbol{{a}}\right)×\boldsymbol{{b}}=\mathrm{0}\:\:?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 63427 by Rio Michael last updated on 04/Jul/19 $$\left(\mathrm{1}\right)\:{A}\:{plane}\:{contains}\:{the}\:{lines}\:\frac{{x}+\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{4}−{y}}{\mathrm{2}}=\frac{{z}−\mathrm{2}}{\mathrm{3}}\:{and}\: \\ $$$${r}=\:\left(\mathrm{2}{i}+\mathrm{2}{j}\:+\:\mathrm{12}{k}\right)+{t}\left(−{i}+\mathrm{2}{j}\:+\mathrm{4}{k}\right).\:{find} \\ $$$$\left({a}\right)\:{the}\:{angle}\:{between}\:{these}\:{lines}. \\ $$$$\left({b}\right)\:{A}\:{cartesian}\:{equation}\:{of}\:{the}\:{plane}. \\ $$$$\left(\mathrm{2}\right)\:{Given}\:{the}\:{lines}\:\boldsymbol{{l}}_{\mathrm{1}} :\frac{{x}−\mathrm{10}}{\mathrm{3}}=\frac{{y}−\mathrm{1}}{\mathrm{1}}=\frac{{z}−\mathrm{9}}{\mathrm{4}}\:\:\boldsymbol{{l}}_{\mathrm{2}} :{r}=\left(−\mathrm{9}{j}+\mathrm{13}{k}\right)+\mu\left({i}+\mathrm{2}{j}−\mathrm{3}{k}\right) \\ $$$${where}\:\mu\:{is}\:{a}\:{parameter};\:\boldsymbol{{l}}_{\mathrm{3}} :\frac{{x}+\mathrm{10}}{\mathrm{4}}=\frac{{y}+\mathrm{5}}{\mathrm{3}}=\frac{{z}+\mathrm{4}}{\mathrm{1}}. \\…
Question Number 128830 by bemath last updated on 10/Jan/21 Answered by liberty last updated on 10/Jan/21 $$\:\mathrm{let}\:\mid\overset{\rightarrow} {{a}}\mid\:=\:\mid\overset{\rightarrow} {{b}}\mid\:=\:\mathrm{1}\:;\:\mathrm{also}\:\mid\:\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid\:=\:\mathrm{1}\: \\ $$$$\:\mathrm{we}\:\mathrm{want}\:\mathrm{to}\:\mathrm{compute}\:\mid\overset{\rightarrow} {{a}}−\overset{\rightarrow} {{b}}\:\mid\:.…
Question Number 128347 by mathocean1 last updated on 06/Jan/21 $${E}\:{is}\:{a}\:{vectorial}\:{space}\:{wich}\:{has}\:{as}\:{base}\: \\ $$$$\left(\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}},\overset{\rightarrow} {{k}}\right).\: \\ $$$${P}=\left\{\begin{pmatrix}{{x}}\\{{y}}\\{\:{z}}\end{pmatrix}\:{such}\:{that}\:\mathrm{5}{x}+{y}+{z}=\mathrm{0}\right\} \\ $$$$\mathrm{1}.\:{Determinate}\:{one}\:{base}\:{of}\:{P}. \\ $$ Terms of Service Privacy…
Question Number 128314 by 676597498 last updated on 06/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\mathrm{px}\right)}{\:\sqrt{\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\forall\mathrm{p}\in\mathbb{R} \\ $$ Answered by Dwaipayan Shikari last updated on 06/Jan/21 $$\int_{\mathrm{0}}…
Question Number 128245 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\:::\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {xcot}\left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\left({G}+\frac{\pi}{\mathrm{4}}{log}\left(\mathrm{2}\right)\right) \\ $$ Answered by Dwaipayan Shikari last updated on 05/Jan/21 $$\int_{\mathrm{0}}…
Question Number 62624 by Jmasanja last updated on 23/Jun/19 Answered by MJS last updated on 23/Jun/19 $$\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{same}\:\mathrm{as}\:\mathrm{before},\:\mathrm{they}\:\mathrm{all}\:\mathrm{are}\:\mathrm{similar} \\ $$$${P}=\begin{pmatrix}{\mathrm{9cos}\:\mathrm{270}°}\\{\mathrm{9sin}\:\mathrm{270}°}\end{pmatrix}\:\:{Q}=\begin{pmatrix}{\mathrm{10cos}\:\mathrm{45}°}\\{\mathrm{10sin}\:\mathrm{45}°}\end{pmatrix}\:\:{R}=\begin{pmatrix}{\mathrm{10cos}\:\mathrm{135}°}\\{\mathrm{10sin}\:\mathrm{135}°}\end{pmatrix} \\ $$$${P}=\begin{pmatrix}{\mathrm{0}}\\{−\mathrm{9}}\end{pmatrix}\:\:{Q}=\begin{pmatrix}{\mathrm{5}\sqrt{\mathrm{2}}}\\{\mathrm{5}\sqrt{\mathrm{2}}}\end{pmatrix}\:\:{R}=\begin{pmatrix}{−\mathrm{5}\sqrt{\mathrm{2}}}\\{\mathrm{5}\sqrt{\mathrm{2}}}\end{pmatrix} \\ $$$${P}+{Q}+{R}=\begin{pmatrix}{\mathrm{0}}\\{\mathrm{10}\sqrt{\mathrm{2}}−\mathrm{9}}\end{pmatrix} \\ $$…