Question Number 9715 by tawakalitu last updated on 28/Dec/16 $$\mathrm{Vector}\:\overset{\rightarrow} {\mathrm{A}}\:\mathrm{of}\:\mathrm{magnitude}\:\mathrm{20}\:\mathrm{unit},\:\mathrm{lies}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{direction}\:\mathrm{45}°\mathrm{S}\:\mathrm{of}\:\mathrm{E}\:\mathrm{while}\:\mathrm{vector}\:\overset{\rightarrow} {\mathrm{B}}\:\mathrm{of}\:\mathrm{magnitude} \\ $$$$\mathrm{30}\:\mathrm{units}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{60}°\mathrm{W}\:\mathrm{of}\:\mathrm{N}. \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{scaler}\:\mathrm{product}\:\:\overset{\rightarrow} {\mathrm{A}}\centerdot\overset{\rightarrow} {\mathrm{B}} \\ $$ Answered by sandy_suhendra…
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Question Number 140690 by liberty last updated on 11/May/21 $$\:\mathrm{Vector}\: \\ $$$$\mathrm{let}\:\mathcal{L}_{\mathrm{1}} =\:\mathrm{AC}\:\mathrm{where}\:\mathrm{A}=\left(\mathrm{2},−\mathrm{1},\mathrm{3}\right)\:\mathrm{and} \\ $$$$\mathrm{C}=\left(\mathrm{1},\mathrm{0},−\mathrm{5}\right)\mathrm{and}\:\mathrm{let}\:\mathcal{L}_{\mathrm{2}} =\:\mathrm{BD}\:\mathrm{where} \\ $$$$\mathrm{B}=\left(\mathrm{1},\mathrm{3},\mathrm{0}\right)\:\mathrm{and}\:\mathrm{D}=\left(\mathrm{3},−\mathrm{4},\mathrm{1}\right).\:\mathrm{Determine} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathcal{L}_{\mathrm{1}} \:\mathrm{and}\:\mathcal{L}_{\mathrm{2}} . \\ $$ Answered…
Find-the-coordinates-of-2-0-when-the-axes-are-rotated-counterclockwise-through-the-angle-arcsin-4-5-
Question Number 140666 by john_santu last updated on 11/May/21 $${Find}\:{the}\:{coordinates}\:{of}\:\left(−\mathrm{2},\mathrm{0}\right)\: \\ $$$${when}\:{the}\:{axes}\:{are}\:{rotated}\:{counterclockwise} \\ $$$${through}\:{the}\:{angle}\:\mathrm{arcsin}\:\frac{\mathrm{4}}{\mathrm{5}}. \\ $$ Answered by bemath last updated on 11/May/21 $$\begin{cases}{\mathrm{x}'=\mathrm{x}\:\mathrm{cos}\:\theta−\mathrm{ysin}\:\theta}\\{\mathrm{y}'=\mathrm{xsin}\:\theta+\mathrm{ycos}\:\theta}\end{cases} \\…
Question Number 9553 by tawakalitu last updated on 14/Dec/16 $$\mathrm{Find}\::\:\:\:\mathrm{u}\centerdot\mathrm{v} \\ $$$$\left(\mathrm{i}\right)\:\:\:\mathrm{f}\left(\mathrm{z}\right)\:=\:\mid\mathrm{z}\mid^{\mathrm{2}} \\ $$$$\left(\mathrm{ii}\right)\:\:\mathrm{f}\left(\mathrm{z}\right)\:=\:\mathrm{z}\:+\:\frac{\mathrm{1}}{\mathrm{z}} \\ $$ Commented by geovane10math last updated on 14/Dec/16 $${z}\:\mathrm{is}\:\mathrm{complex}\:? \\…
Question Number 140502 by benjo_mathlover last updated on 08/May/21 $$\mathrm{If}\:\mathrm{three}\:\mathrm{vector}\:\overset{\rightarrow} {\mathrm{a}}\:,\:\overset{\rightarrow} {\mathrm{b}}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{c}}\:\mathrm{are}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{a}}\:\neq\:\mathrm{0}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{b}}\:=\:\mathrm{2}\left(\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{c}}\right) \\ $$$$,\mid\overset{\rightarrow} {\mathrm{a}}\mid\:=\:\mid\overset{\rightarrow} {\mathrm{c}}\mid\:=\:\mathrm{1}\:,\:\mid\overset{\rightarrow} {\mathrm{b}}\mid\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{the}\:…
Question Number 9254 by tawakalitu last updated on 25/Nov/16 Answered by mrW last updated on 26/Nov/16 $$\mathrm{2cos}\:\pi\mathrm{t}=\mathrm{x} \\ $$$$\mathrm{y}=\mathrm{1}−\mathrm{4cos}\:\mathrm{2}\pi\mathrm{t}=\mathrm{1}−\mathrm{4}\left(\mathrm{2cos}\:^{\mathrm{2}} \pi\mathrm{t}−\mathrm{1}\right) \\ $$$$\mathrm{y}=\mathrm{5}−\mathrm{2}\left(\mathrm{2cos}\:\pi\mathrm{t}\right)^{\mathrm{2}} \\ $$$$\mathrm{hence}\:\mathrm{y}=\mathrm{5}−\mathrm{2x}^{\mathrm{2}} \\…
Question Number 9230 by tawakalitu last updated on 24/Nov/16 $$\mathrm{Given}\:\mathrm{that}\: \\ $$$$\mathrm{a}\:=\:\mathrm{2i}\:−\:\mathrm{3j}\:+\:\mathrm{k},\:\mathrm{b}\:=\:\mathrm{4i}\:+\:\mathrm{j}\:−\:\mathrm{3k}, \\ $$$$\mathrm{c}\:=\:\mathrm{i}\:−\:\mathrm{3k} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{a}\centerdot\mathrm{b}\right)\mathrm{c},\:\:\mathrm{a}\left(\mathrm{b}×\mathrm{c}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140176 by EDWIN88 last updated on 05/May/21 $$\mathrm{Let}\:\mathrm{V}\:\mathrm{be}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{space}\:\mathrm{of}\:\mathrm{polynomials} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=\:\mathrm{a}+\mathrm{bx}+\mathrm{cx}^{\mathrm{2}} \:\mathrm{with}\:\mathrm{real}\:\mathrm{coefficients} \\ $$$$\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}.\:\mathrm{Define}\:\mathrm{an}\:\mathrm{inner}\:\mathrm{product}\:\mathrm{on}\:\mathrm{V} \\ $$$$\mathrm{by}\:\left(\mathrm{p},\mathrm{q}\right)=\frac{\mathrm{1}}{\mathrm{2}}\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\mathrm{p}\left(\mathrm{x}\right)\mathrm{q}\left(\mathrm{x}\right)\:\mathrm{dx}\:. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{a}\:\mathrm{orthonormal}\:\mathrm{basis}\:\mathrm{for}\:\mathrm{V}\:\mathrm{consisting} \\ $$$$\mathrm{of}\:\mathrm{polynomials}\:\phi_{\mathrm{o}} \left(\mathrm{x}\right)\:,\:\phi_{\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{and}\:\phi_{\mathrm{2}}…
Question Number 9060 by tawakalitu last updated on 16/Nov/16 Answered by mrW last updated on 17/Nov/16 $$\left.{b}\right) \\ $$$$\mathrm{60}^{\mathrm{2}} =\mathrm{40}^{\mathrm{2}} +\mathrm{92}^{\mathrm{2}} −\mathrm{2}×\mathrm{40}×\mathrm{92}×\mathrm{cos}\:\alpha \\ $$$$\mathrm{cos}\:\alpha=\frac{\mathrm{40}^{\mathrm{2}} +\mathrm{92}^{\mathrm{2}}…