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Question Number 168121 by rexford last updated on 03/Apr/22

Answered by FelipeLz last updated on 04/Apr/22

r^→ = (a, b, c) {: ((r^→ ∙ı^� = a)),((r^→ ∙ȷ^� = b)),((r^→ ∙k^� = c)) } a = b = c = m ∣r^→ ∣ = 3 (√(a^2 +b^2 +c^2 )) = (√(3m^2 )) = 3 3m^2 = 9 m = ±(√3) ∴ r^→ = ±(√3)(1, 1, 1)

$$\overset{\rightarrow} {{r}}\:=\:\left({a},\:{b},\:{c}\right) \\ $$$$\left.\begin{matrix}{\overset{\rightarrow} {{r}}\centerdot\hat {\imath}\:=\:{a}}\\{\overset{\rightarrow} {{r}}\centerdot\hat {\jmath}\:=\:{b}}\\{\overset{\rightarrow} {{r}}\centerdot\hat {{k}}\:=\:{c}}\end{matrix}\right\}\:{a}\:=\:{b}\:=\:{c}\:=\:{m} \\ $$$$\mid\overset{\rightarrow} {{r}}\mid\:=\:\mathrm{3}\: \\ $$$$\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }\:=\:\sqrt{\mathrm{3}{m}^{\mathrm{2}} }\:=\:\mathrm{3} \\ $$$$\mathrm{3}{m}^{\mathrm{2}} \:=\:\mathrm{9} \\ $$$${m}\:=\:\pm\sqrt{\mathrm{3}}\:\therefore\:\overset{\rightarrow} {{r}}\:=\:\pm\sqrt{\mathrm{3}}\left(\mathrm{1},\:\mathrm{1},\:\mathrm{1}\right) \\ $$

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