Question Number 71986 by rajesh4661kumar@gmail.com last updated on 23/Oct/19 Answered by mind is power last updated on 23/Oct/19 $$\mathrm{not}\:\mathrm{unique}\:\mathrm{angle} \\ $$$$\mathrm{XY}=\left\{\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\in\mathbb{R}^{\mathrm{3}} :\mathrm{z}=\mathrm{0}\right\} \\ $$$$\mathrm{angle}\:\mathrm{between}\:\mathrm{vecror}\:\mathrm{and}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{not}\:\mathrm{defind}\: \\…
Question Number 6374 by sanusihammed last updated on 25/Jun/16 $${Show}\:{that} \\ $$$$\overset{−} {{a}}\:×\:\left({b}\:×\:{c}\right)\:=\:\left(\overset{−} {{a}}\:.\:\overset{−} {{c}}\right)\overset{−} {{b}}\:\:−\:\:\left(\overset{−} {{a}}\:.\:\overset{−} {{b}}\right)\overset{−} {{c}} \\ $$ Commented by FilupSmith last…
Question Number 6321 by sanusihammed last updated on 23/Jun/16 $${Determine}\:\in\:{and}\:{N}\:{by}\:{using}\:{vector}\:{such}\:{that}\:{point}\:\left(−\mathrm{1},\mathrm{3},\mathrm{2}\right), \\ $$$$\left(−\mathrm{4},−\mathrm{2},−\mathrm{2}\right)\:{and}\:\left(\mathrm{5},\in,{N}\right)\:{lies}\:{on}\:{a}\:{straight}\:{line} \\ $$$$ \\ $$ Answered by nburiburu last updated on 23/Jun/16 $${let}'{s}\:{find}\:{the}\:{line}: \\…
Question Number 136300 by liberty last updated on 20/Mar/21 $${Let}\:{vector}\:\overset{\rightarrow} {{a}}\:,\:\overset{\rightarrow} {{b}}\:{and}\:\overset{\rightarrow} {{c}}\:{such}\:{that} \\ $$$$\mid\overset{\rightarrow} {{a}}\mid=\mid\overset{\rightarrow} {{b}}\mid=\frac{\mid\overset{\rightarrow} {{c}}\mid}{\mathrm{2}}\:{and}\:\overset{\rightarrow} {{a}}×\left(\overset{\rightarrow} {{a}}×\overset{\rightarrow} {{c}}\right)+\overset{\rightarrow} {{b}}=\mathrm{0} \\ $$$${find}\:{the}\:{acute}\:{angle}\:{between}\:\overset{\rightarrow} {{a}}\:{and}\:\overset{\rightarrow}…
Question Number 135965 by liberty last updated on 17/Mar/21 $${Vector} \\ $$Three vectors satisfy a.b = b.c = c.a = -1 and a + b…
Question Number 135821 by mnjuly1970 last updated on 16/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:\:…..\:\:\:{calculus}….\: \\ $$$$\:\:\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}−\sqrt{\mathrm{1}−{x}}}\right){dx}=\mathrm{4}\left(\mathrm{1}−\zeta\left(\mathrm{2}\right)\right) \\ $$$$ \\ $$ Answered by mathmax by abdo…
Question Number 135790 by benjo_mathlover last updated on 16/Mar/21 $${Find}\:{the}\:{component}\:{form}\:{of} \\ $$$${the}\:{vector}\:{that}\:{reprecents}\:{the} \\ $$$${velocity}\:{of}\:{an}\:{airplane}\:{descending} \\ $$$${at}\:{speed}\:{of}\:\mathrm{150}\:{miles}\:{per}\:{hour} \\ $$$${at}\:{angle}\:\mathrm{20}°\:{below}\:{the}\:{horizontal} \\ $$ Terms of Service Privacy Policy…
Question Number 4548 by Yozzii last updated on 07/Feb/16 Commented by Yozzii last updated on 07/Feb/16 $${In}\:{the}\:{diagram}\:{is}\:{a}\:{parallelogram}\:{ABCD} \\ $$$${with}\:{diagonal}\:{CB}. \\ $$$${E}\:{and}\:{F}\:{are}\:{the}\:{midpoints}\:{of}\:{CD}\:{and} \\ $$$${BD}\:{respectively}.\:{Using}\:{vectors},\:{prove} \\ $$$${that}\:{AE}\:{and}\:{AF}\:{trisect}\:{CB}.…
Question Number 135423 by benjo_mathlover last updated on 13/Mar/21 $${If}\:\overset{\rightarrow} {{a}}=\left(\mathrm{4},\mathrm{2},−\mathrm{1}\right),\:\overset{\rightarrow} {{b}}=\left({m},\mathrm{1},\mathrm{1}\right) \\ $$$$\overset{\rightarrow} {{c}}=\left(\bar {\mathrm{3}}−\mathrm{1},\mathrm{0}\right)\:{are}\:{three}\:{vectors} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:{m}\:{such} \\ $$$${that}\:\overset{\rightarrow} {{a}},\overset{\rightarrow} {{b}}\:{and}\:\overset{\rightarrow} {{c}}\:{are}\:{coplanar}\:{and} \\ $$$${find}\:\overset{\rightarrow}…
Question Number 69620 by aseer imad last updated on 25/Sep/19 Commented by kaivan.ahmadi last updated on 26/Sep/19 $${b}\:{is}\:{answer}\:{since}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{5}}\left(\mathrm{4},\mathrm{0},−\mathrm{3}\right).\left(\mathrm{3},−\mathrm{1},\mathrm{4}\right)=\frac{\mathrm{1}}{\mathrm{5}}\left(\mathrm{12}+\mathrm{0}−\mathrm{12}\right)=\mathrm{0}\Rightarrow\overset{\rightarrow} {{b}}\:{is} \\ $$$${perpendicular}\:{to}\:\mathrm{3}{i}−{j}+\mathrm{4}{k} \\ $$$${and}…