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makkiz [27]
2 years ago
6

*Be sure to simplify fractions and rationalize denominators if necessary.

Mathematics
1 answer:
m_a_m_a [10]2 years ago
6 0

As given by the question

There are given that the vector:

\vec{v}=\vec{2i}+\vec{3j}

Now,

From the formula to find the unit vector in same direction is:

\vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert}

Then,

\begin{gathered} \vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\vec{2i}+\vec{3j}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\sqrt[]{2^2+3^2}\rvert} \end{gathered}

Then,

\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{2^2+3^2}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{4+9}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \end{gathered}

Then,

Rationalize the denominator:

So,

\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}}\times\frac{\sqrt[]{13}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{\sqrt[]{13}(2i}+\vec{3j})}{13} \\ \vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j \end{gathered}

Hence, the unit vector is shown below:

\vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j

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The radius of the hemisphere is 9.5 inches.

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