Question Number 195165 by Nimnim111118 last updated on 25/Jul/23 $$\mathrm{If}\:\overset{\rightarrow} {\mathrm{r}_{\mathrm{1}} }=\left(\mathrm{sin}\theta,\mathrm{cos}\theta,\theta\right),\:\overset{\rightarrow} {\mathrm{r}_{\mathrm{2}} }=\left(\mathrm{cos}\theta,−\mathrm{sin}\theta,−\mathrm{3}\right)\:\mathrm{and} \\ $$$$\:\overset{\rightarrow} {\mathrm{r}_{\mathrm{3}} }=\left(\mathrm{2},\mathrm{3},−\mathrm{1}\right),\:\mathrm{find}\:\frac{\mathrm{d}}{\mathrm{d}\theta}\left\{\overset{\rightarrow} {\mathrm{r}_{\mathrm{1}} }×\left(\overset{\rightarrow} {\mathrm{r}_{\mathrm{2}} }×\overset{\rightarrow} {\mathrm{r}_{\mathrm{3}} }\right)\right\}\:\mathrm{at}\:\theta=\mathrm{0} \\…
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Question Number 194600 by byaw last updated on 10/Jul/23 $$ \\ $$An object is pulled up a smooth plane inclined at angle 45° to the…
Question Number 194602 by byaw last updated on 10/Jul/23 $$ \\ $$A ball is thrown vertically upwards with a velocity of 10m/s from a point…
Question Number 194497 by Biteshwar last updated on 08/Jul/23 $$\mathrm{12th} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Commented by Frix last updated…
Question Number 193809 by byaw last updated on 20/Jun/23 A(-1, 2), B(3, 5) and C(4, 8) are the vertices of triangle ABC. Forces whose magnitudes…
Question Number 130889 by mnjuly1970 last updated on 30/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:\:{advanced}\:\:{mathematcs}\:\:… \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{1}+{n}^{\mathrm{2}} }\:=\frac{{csch}\left(\pi\right)−\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$ Answered by mindispower…
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Question Number 130537 by benjo_mathlover last updated on 26/Jan/21 Answered by EDWIN88 last updated on 26/Jan/21 $$\Leftrightarrow\:\overset{\rightarrow} {{a}}×\left(\overset{\rightarrow} {{b}}×\overset{\rightarrow} {{c}}\right)=\left(\overset{\rightarrow} {{a}}.\overset{\rightarrow} {{c}}\right)\overset{\rightarrow} {{b}}−\left(\overset{\rightarrow} {{a}}.\overset{\rightarrow} {{b}}\right)\overset{\rightarrow}…
Question Number 130523 by benjo_mathlover last updated on 26/Jan/21 Answered by TheSupreme last updated on 26/Jan/21 $${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}}…