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Category: Vector

If-vector-a-b-c-0-a-7-b-3-and-c-5-find-the-angle-vector-a-and-c-

Question Number 117543 by bemath last updated on 12/Oct/20 $$\mathrm{If}\:\mathrm{vector}\:\overset{\rightarrow} {\mathrm{a}}+\overset{\rightarrow} {\mathrm{b}}+\overset{\rightarrow} {\mathrm{c}}=\mathrm{0} \\ $$$$\mid\overset{\rightarrow} {\mathrm{a}}\mid=\mathrm{7},\:\mid\overset{\rightarrow} {\mathrm{b}}\mid=\mathrm{3}\:\mathrm{and}\:\mid\overset{\rightarrow} {\mathrm{c}}\mid=\mathrm{5} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{vector}\:\overset{\rightarrow} {\mathrm{a}}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{c}}\:? \\ $$ Answered…

Help-me-The-rate-of-change-of-w-x-3-y-2-z-y-3-z-2-xz-4-at-the-point-Q-0-1-2-in-the-direction-V-2i-j-2k-is-a-2-b-3-c-4-d-No-alternati

Question Number 182438 by neinhaltsieger369 last updated on 09/Dec/22 $$\: \\ $$$$\:\left[\boldsymbol{\mathrm{Help}}\:\:\boldsymbol{\mathrm{me}}!\right] \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{The}}\:\:\boldsymbol{\mathrm{rate}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{change}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{w}}\:\:=\:\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} \boldsymbol{\mathrm{y}}^{\mathrm{2}} \boldsymbol{\mathrm{z}}\:\:+\:\boldsymbol{\mathrm{y}}^{\mathrm{3}} \boldsymbol{\mathrm{z}}^{\mathrm{2}} \:−\:\boldsymbol{\mathrm{xz}}^{\mathrm{4}} \:\:\boldsymbol{\mathrm{at}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{point}}\:\:\boldsymbol{\mathrm{Q}}\left(\mathrm{0},\:\mathrm{1},\:\mathrm{2}\right) \\ $$$$\:\boldsymbol{\mathrm{in}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{direction}}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{V}}}\:\:=\:\:\mathrm{2}\boldsymbol{\mathrm{i}}\:\:+\:\:\boldsymbol{\mathrm{j}}\:\:+\:\:\mathrm{2}\boldsymbol{\mathrm{k}}\:\:\boldsymbol{\mathrm{is}}: \\…

If-P-2-j3-and-Q-2-j3-and-R-j1-Show-that-angle-PRQ-is-right-angle-

Question Number 51263 by Tawa1 last updated on 25/Dec/18 $$\mathrm{If}\:\:\mathrm{P}\:=\:\mathrm{2}\:+\:\mathrm{j3}\:\mathrm{and}\:\mathrm{Q}\:=\:\mathrm{2}\:−\:\mathrm{j3}\:\mathrm{and}\:\mathrm{R}\:=\:\mathrm{j1} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\:\mathrm{angle}\:\:\mathrm{PRQ}\:\mathrm{is}\:\mathrm{right}\:\mathrm{angle} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18 $${P}\left(\mathrm{2},\mathrm{3}\right)\:\:\:{Q}\left(\mathrm{2},−\mathrm{3}\right)\:\:\:{R}\left(\mathrm{0},\mathrm{1}\right) \\ $$$${PQ}=\mathrm{6}\:\:\:\:{QR}=\sqrt{\mathrm{2}^{\mathrm{2}} +\left(−\mathrm{4}\right)^{\mathrm{2}}…