Write the vector v in terms of i and j whose magnitude and direction angle θ are given. = 8, θ = 30°a. v = 4i + 4sqrt3jb. v = -4sqrt3i + 4jc. v = 4sqrt3i + 4jd. v = 4sqrt2i + 4sqrt2j
Question
Answer:
[tex]\bf \begin{cases}
r=8\\
\theta =30^o
\end{cases}\qquad \qquad \qquad \qquad
\begin{cases}
tan(\theta )=\frac{b}{a}\\
r^2=a^2+b^2
\end{cases}\\\\
-------------------------------\\\\
tan(30^o)=\cfrac{b}{a}\implies \cfrac{\quad\frac{1}{2} \quad }{\frac{\sqrt{3}}{2}}=\cfrac{b}{a}\implies \cfrac{1}{\sqrt{3}}=\cfrac{b}{a}\implies \boxed{\cfrac{a}{\sqrt{3}}=b}\\\\
-------------------------------[/tex][tex]\bf 8^2=a^2+b^2\implies 64=a^2+b^2\implies 64=a^2+\left( \boxed{\cfrac{a}{\sqrt{3}}} \right)^2 \\\\\\ 64=a^2+\cfrac{a^2}{3}\implies 64=\cfrac{4a^2}{3}\implies 16=\cfrac{a^2}{3}\implies 48=a^2 \\\\\\ \sqrt{48}=a\implies \boxed{4\sqrt{3}=a}\\\\ -------------------------------\\\\ \cfrac{a}{\sqrt{3}}=b\implies \cfrac{4\sqrt{3}}{\sqrt{3}}=b\implies \boxed{4=b}\\\\ -------------------------------\\\\ v~=~4\sqrt{3}i~+~4j[/tex]
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10 months ago
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