Menu Close

Category: Vector

Solve-z-4-16-

Question Number 12442 by tawa last updated on 22/Apr/17 $$\mathrm{Solve}:\:\:\:\mathrm{z}^{\mathrm{4}} \:=\:−\:\mathrm{16} \\ $$ Answered by ajfour last updated on 22/Apr/17 $${z}^{\mathrm{4}} =\mathrm{2}^{\mathrm{4}} {e}^{{i}\left(\pi+\mathrm{2}{k}\pi\right)} \\ $$$${z}=\mathrm{2}{e}^{{i}\left(\frac{\pi}{\mathrm{4}}+\frac{\mathrm{2}{k}\pi}{\mathrm{4}}\:\right)}…

ABC-is-any-triangle-C-B-A-are-respectively-middles-of-AB-AC-and-BC-we-suppose-that-AB-c-AC-b-BC-a-1-u-a-2-BC-b-2-C-A-c-2-AB-is-a-vector-Demonstrate-that-u

Question Number 77745 by mathocean1 last updated on 09/Jan/20 $$\mathrm{ABC}\:\mathrm{is}\:\mathrm{any}\:\mathrm{triangle}. \\ $$$$\mathrm{C}'\:.\:\mathrm{B}'\:\:.\mathrm{A}'\:\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{middles} \\ $$$$\mathrm{of}\:\left[\mathrm{AB}\right]\:.\:\left[\mathrm{AC}\right]\:\:\mathrm{and}\:\:\left[\mathrm{BC}\right]. \\ $$$$\mathrm{we}\:\mathrm{suppose}\:\mathrm{that}\: \\ $$$$\mathrm{AB}=\mathrm{c}\:\:\:\mathrm{AC}=\mathrm{b}\:\:\:\:\mathrm{BC}=\mathrm{a}. \\ $$$$\left.\mathrm{1}\right)\:\overset{\rightarrow\:} {\mathrm{u}}=\mathrm{a}^{\mathrm{2}} \mathrm{B}\overset{\rightarrow} {\mathrm{C}}+\mathrm{b}^{\mathrm{2}\:} \overset{\rightarrow} {\mathrm{C}A}+\mathrm{c}^{\mathrm{2}}…

Question-143127

Question Number 143127 by liberty last updated on 10/Jun/21 Answered by EDWIN88 last updated on 11/Jun/21 $$\:\mathrm{Let}\:\begin{cases}{\overset{\rightarrow} {\mathrm{a}}=\mathrm{QR}=\left(\mathrm{1},\mathrm{3},−\mathrm{1}\right)}\\{\overset{\rightarrow} {\mathrm{b}}=\mathrm{QS}=\left(−\mathrm{3},\mathrm{2},\mathrm{3}\right)}\\{\overset{\rightarrow} {\mathrm{c}}=\mathrm{QP}=\left(\mathrm{0},\mathrm{3},\mathrm{3}\right)}\end{cases} \\ $$$$\mathrm{distance}\:\mathrm{d}\:\mathrm{from}\:\mathrm{P}\:\mathrm{to}\:\mathrm{plane}\:\mathrm{is}\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{d}\:=\:\frac{\mid\overset{\rightarrow} {\mathrm{a}}.\left(\overset{\rightarrow}…

CALCULUS-prove-that-n-1-1-n-1-n-1-2-2n-2log-2-golden-ratio-

Question Number 142970 by mnjuly1970 last updated on 08/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:……….{CALCULUS}……….. \\ $$$$\:\:\:\:\:\:\:{prove}\:{that}::\:\: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \left(\left({n}−\mathrm{1}\right)!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}\right)!}=\mathrm{2}{log}^{\mathrm{2}} \left(\varphi\right) \\ $$$$\:\:\:\:\varphi={golden}\:{ratio}…. \\ $$$$\:\:\:\:…………. \\ $$…

Question-142927

Question Number 142927 by bramlexs22 last updated on 07/Jun/21 Answered by Olaf_Thorendsen last updated on 07/Jun/21 $$\mathrm{Let}\:\left(\mathrm{C},\:\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}}\right) \\ $$$$\mathrm{with}\:\mathrm{C}\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix} \\ $$$$\mathrm{G}\begin{pmatrix}{{c}_{\mathrm{2}} }\\{\mathrm{0}}\end{pmatrix}\:=\:{c}_{\mathrm{2}} \overset{\rightarrow}…

The-plan-is-provided-with-an-orthonormal-reference-O-I-J-the-following-points-are-given-A-1-2-B-2-3-C-1-9-We-assume-that-the-point-O-is-the-barycenter-of-the-point-A-B-C-O-bar-A-3-B-1-

Question Number 77356 by mathocean1 last updated on 05/Jan/20 $$\mathrm{The}\:\mathrm{plan}\:\mathrm{is}\:\mathrm{provided}\:\mathrm{with}\:\mathrm{an}\: \\ $$$$\mathrm{orthonormal}\:\mathrm{reference}\:\left(\:\mathrm{O}.\mathrm{I}.\mathrm{J}\right). \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{points}\:\mathrm{are}\:\mathrm{given} \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{2}\right)\:\mathrm{B}\left(−\mathrm{2},\mathrm{3}\right)\:\mathrm{C}\left(\mathrm{1},\mathrm{9}\right). \\ $$$$\mathrm{We}\:\mathrm{assume}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{barycenter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\mathrm{A},\mathrm{B},\mathrm{C}. \\ $$$$\rightarrow\mathrm{O}=\mathrm{bar}\left\{\left(\mathrm{A};\mathrm{3}\right),\left(\mathrm{B};\mathrm{1}\right),\left(\mathrm{C};−\mathrm{1}\right)\right\} \\ $$$$ \\…

Determiner-et-construire-l-ensemble-des-points-M-tel-que-3MA-2-MB-2-MC-2-42-Le-plan-est-muni-d-un-repere-orthonorme-O-I-J-A-1-2-B-2-3-C-1-9-on-considere-que-O-barycentre-A-3-B-1-

Question Number 77296 by mathocean1 last updated on 05/Jan/20 $$\mathrm{Determiner}\:\mathrm{et}\:\mathrm{construire}\:\mathrm{l}.\mathrm{ensemble} \\ $$$$\mathrm{des}\:\mathrm{points}\:\mathrm{M}\:\mathrm{tel}\:\mathrm{que}: \\ $$$$\mathrm{3MA}^{\mathrm{2}} +\mathrm{MB}^{\mathrm{2}} −\mathrm{MC}^{\mathrm{2}} =−\mathrm{42} \\ $$$$\mathrm{Le}\:\mathrm{plan}\:\mathrm{est}\:\mathrm{muni}\:\mathrm{d}.\mathrm{un}\:\mathrm{repere}\: \\ $$$$\mathrm{orthonorme}\:\left(\mathrm{O},\mathrm{I},\mathrm{J}\right) \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{2}\right)\:\:\:\mathrm{B}\left(−\mathrm{2},\mathrm{3}\right)\:\:\mathrm{C}\left(\mathrm{1},\mathrm{9}\right). \\ $$$$\mathrm{on}\:\mathrm{considere}\:\mathrm{que}\:…

Find-the-magnitude-of-two-forces-such-that-if-they-act-at-right-angle-their-resultant-is-10-and-13-if-they-act-at-an-angle-of-60-

Question Number 11405 by tawa last updated on 24/Mar/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{such}\:\mathrm{that}\:\mathrm{if}\:\mathrm{they}\:\mathrm{act}\:\mathrm{at}\:\mathrm{right}\:\mathrm{angle}\:\mathrm{their} \\ $$$$\mathrm{resultant}\:\mathrm{is}\:\sqrt{\mathrm{10}}\:,\:\mathrm{and}\:\sqrt{\mathrm{13}}\:\mathrm{if}\:\mathrm{they}\:\mathrm{act}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{60}°.\: \\ $$ Answered by mrW1 last updated on 24/Mar/17 $${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{10} \\…