Mathematics: Could someone me find the magnitude and degrees of the vectors with the given information. 12i + 4sqrt3j

Could someone me find the magnitude and degrees

Ответ:

cloeybrown

14.03.2022

$\bf \stackrel{a}{12}i+\stackrel{b}{4\sqrt{3}}j\implies \ \textless \ 12~,~4\sqrt{3}\ \textgreater \ \qquad 
\begin{cases}
\stackrel{magnitude}{r}=\sqrt{a^2+b^2}\\\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}\\\\
-------------------------------\\\\
r=\sqrt{12^2+(4\sqrt{3})^2}\implies r=\sqrt{144+(4^2\sqrt{3^2})}$

$\bf r=\sqrt{144+(16\cdot 3)}\implies r=\sqrt{144+48}\implies r=\sqrt{192}
\\\\\\
r=\sqrt{64\cdot 3}\implies r=\sqrt{8^2\cdot 3}\implies r=8\sqrt{3}\\\\
-------------------------------\\\\
\theta =tan^{-1}\left( \cfrac{4\sqrt{3}}{12} \right)\implies \theta =tan^{-1}\left( \cfrac{\sqrt{3}}{3} \right)\implies \theta =
\begin{cases}
\frac{\pi }{6}\leftarrow \\\\
\frac{7\pi }{6}
\end{cases}$

notice, those two angles have a valid tangent value, however, notice the "a" and "b" components, their signs are +a and +b, meaning the angle is in the first quadrant, thus, it has to be angle in the first quadrant then.

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Could someone me find the magnitude and degrees of the vectors with the given information. 12i + 4sqrt3j

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