367,576 views
34 votes
34 votes
*Be sure to simplify fractions and rationalize denominators if necessary.

*Be sure to simplify fractions and rationalize denominators if necessary.-example-1
User Mkk
by
2.3k points

1 Answer

10 votes
10 votes

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}}*\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

User TheBlackKeys
by
2.8k points