Menu Close

Category: Vector

Find-the-distance-from-the-point-S-1-1-5-to-the-line-L-x-1-t-y-3-t-z-2t-

Question Number 123876 by john_santu last updated on 29/Nov/20 $${Find}\:{the}\:{distance}\:{from}\:{the}\: \\ $$$${point}\:{S}\left(\mathrm{1},\mathrm{1},\mathrm{5}\right)\:{to}\:{the}\:{line}\: \\ $$$${L}\::\:\begin{cases}{{x}=\mathrm{1}+{t}}\\{{y}=\mathrm{3}−{t}\:}\\{{z}=\mathrm{2}{t}}\end{cases}. \\ $$ Answered by mr W last updated on 29/Nov/20 $${Method}\:{I}…

Show-that-the-angle-between-two-unit-vectors-a-and-b-is-given-by-cos-a-b-Hence-given-that-a-i-cosA-j-sinA-and-b-i-cosB-j-sinB-prove-that-cos-A-B-cos

Question Number 58312 by pete last updated on 21/Apr/19 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{angle}\:\theta\:\mathrm{between}\:\mathrm{two}\:\mathrm{unit} \\ $$$$\mathrm{vectors}\:\underset{} {\hat {\mathrm{a}}}\:\mathrm{and}\:\underset{} {\hat {\mathrm{b}}}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{cos}\theta=\underset{} {\hat {\mathrm{a}}}\bullet\underset{} {\hat {\mathrm{b}}}. \\ $$$$\mathrm{Hence},\:\mathrm{given}\:\mathrm{that}\:\underset{} {\hat {\mathrm{a}}}=\underset{} {\mathrm{i}cosA}+\underset{}…

x-4-x-3-38x-2-31x-45-x-5-

Question Number 58090 by smiak8742 last updated on 17/Apr/19 $$\left({x}^{\mathrm{4}} −{x}^{\mathrm{3}} −\mathrm{38}{x}^{\mathrm{2}} −\mathrm{31}{x}+\mathrm{45}\right)\boldsymbol{\div}\left({x}+\mathrm{5}\right) \\ $$ Answered by Kunal12588 last updated on 17/Apr/19 $$\mathrm{625}+\mathrm{125}−\mathrm{950}+\mathrm{155}+\mathrm{45}=\mathrm{0} \\ $$$${x}^{\mathrm{3}}…

n-1-2-n-

Question Number 123115 by 676597498 last updated on 23/Nov/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{n}} =? \\ $$ Commented by Dwaipayan Shikari last updated on 23/Nov/20 $${It}\:{diverges}\:\rightarrow\infty\:\:\:\:\:{as}\:\mid{a}\mid=\mathrm{2} \\…

sec-4-2xdx-

Question Number 57572 by cesar.marval.larez@gmail.com last updated on 07/Apr/19 $$\int\mathrm{sec}^{\mathrm{4}} \mathrm{2xdx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 07/Apr/19 $$\int{sec}^{\mathrm{2}} \mathrm{2}{x}×{sec}^{\mathrm{2}} \mathrm{2}{xdx} \\ $$$$\int\left(\mathrm{1}+{tan}^{\mathrm{2}}…

let-S-be-the-sets-be-the-sequences-of-lenght-2018-whose-terms-are-in-the-sets-1-2-3-4-5-6-10-and-sum-to-3860-prove-that-the-cardinality-of-S-is-at-most-2-386

Question Number 188295 by normans last updated on 27/Feb/23 $$ \\ $$$$\:\:\:\:\boldsymbol{{let}}\:\:\boldsymbol{{S}}\:\boldsymbol{{be}}\:\boldsymbol{{the}}\:\boldsymbol{{sets}}\:\boldsymbol{{be}}\:\boldsymbol{{the}}\:\boldsymbol{{sequences}}\:\boldsymbol{{of}}\:\boldsymbol{{lenght}}\:\mathrm{2018}\:\:\: \\ $$$$\:\:\:\boldsymbol{{whose}}\:\boldsymbol{{terms}}\:\boldsymbol{{are}}\:\boldsymbol{{in}}\:\boldsymbol{{the}}\:\boldsymbol{{sets}}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{10}\right\}\:\boldsymbol{{and}}\:\boldsymbol{{sum}}\:\boldsymbol{{to}}\:\mathrm{3860}.\:\:\: \\ $$$$\:\:\:\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{cardinality}}\:\boldsymbol{{of}}\:\boldsymbol{{S}}\:\boldsymbol{{is}}\:\boldsymbol{{at}}\:\boldsymbol{{most}}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{3860}} \centerdot\left(\:\frac{\mathrm{2018}}{\mathrm{2048}}\right)^{\mathrm{2018}} \\ $$$$ \\ $$$$\:\:\:\: \\ $$…

Question-122579

Question Number 122579 by bramlexs22 last updated on 18/Nov/20 Answered by liberty last updated on 18/Nov/20 $$\left(\mathrm{2a}\right)\:\mathrm{Q}\:\mathrm{symetric}\:\mathrm{if}\:\mathrm{Q}\:=\:\mathrm{Q}^{\mathrm{t}} \\ $$$$\Leftrightarrow\:\begin{pmatrix}{\mathrm{5}\:\:\:\:\:\mathrm{6x}+\mathrm{5y}\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{6}\:\:\:\:\:\:\mathrm{5y}^{\mathrm{2}} −\mathrm{2x}}\\{\mathrm{x}^{\mathrm{2}} −\mathrm{8}\:\:\:\mathrm{3z}\:\:\:\:\:\:\:\:\:\:\:\mathrm{p}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} −\mathrm{8}}\\{\mathrm{6x}+\mathrm{5y}\:\:\:\:\mathrm{6}\:\:\:\:\:\:\:\:\:\:\mathrm{3z}}\\{\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5y}^{\mathrm{2}} −\mathrm{2x}\:\:\:\mathrm{p}}\end{pmatrix} \\ $$$$\mathrm{gives}\:\begin{cases}{\mathrm{6x}+\mathrm{5y}=\mathrm{1}\:\wedge\:\mathrm{x}^{\mathrm{2}}…

Let-W-be-the-subspace-of-R-4-generated-by-vector-1-2-5-3-2-3-1-4-3-8-3-5-find-the-basis-and-dimension-of-W-

Question Number 56899 by Tawa1 last updated on 26/Mar/19 $$\mathrm{Let}\:\:\mathrm{W}\:\:\mathrm{be}\:\mathrm{the}\:\mathrm{subspace}\:\mathrm{of}\:\:\mathbb{R}^{\mathrm{4}} \:\:\mathrm{generated}\:\mathrm{by}\:\mathrm{vector}\: \\ $$$$\left(\mathrm{1},\:−\:\mathrm{2},\:\mathrm{5},\:−\:\mathrm{3}\right),\:\:\:\:\left(\mathrm{2},\:\mathrm{3},\:\mathrm{1},\:−\:\mathrm{4}\right),\:\:\:\left(\mathrm{3},\:\mathrm{8},\:−\:\mathrm{3},\:−\:\mathrm{5}\right)\:\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{basis}\:\mathrm{and}\:\mathrm{dimension}\:\mathrm{of}\:\:\mathrm{W}. \\ $$ Answered by kaivan.ahmadi last updated on 26/Mar/19 $$\begin{vmatrix}{\mathrm{1}\:\:\:\:\:\:\:−\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{5}\:\:\:\:\:\:−\mathrm{3}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:−\mathrm{4}\:\:}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\mathrm{8}\:\:\:\:\:−\mathrm{3}\:\:\:\:\:\:\:−\mathrm{5}}\end{vmatrix}\underset{−\mathrm{3}{R}_{\mathrm{1}}…