## Algebra and Trigonometry 10th Edition

$\lt \dfrac {18}{\sqrt {29}}, \dfrac{ 45}{\sqrt {29}} \gt$
Since $v$ has the same direction as $u$ and since it is a multiple of a unit vector $n$, we can write it as: $\overrightarrow{v} = < 2 n, 5n>$ To find the unit vector, we must first find the magnitude: $\sqrt {((2n)^{2} + (5n)^{2}} = 3$ or, $144 \ n^2+25 \ n^2 =9$ This implies that $n^2=\dfrac{ 81}{29} \implies n=\dfrac{9}{\sqrt {29}}$ Now, $\overrightarrow{v} = < 2 (\dfrac{9}{\sqrt {29}}), 5 (\dfrac{9}{\sqrt {29}})> = \lt \dfrac {18}{\sqrt {29}}, \dfrac{ 45}{\sqrt {29}} \gt$
The passage describes a mathematical problem involving vector calculations and the determination of a unit vector. It provides a step-by-step solution to find the components of the vector.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Algebra and Trigonometry 10th Edition

$\lt \dfrac {18}{\sqrt {29}}, \dfrac{ 45}{\sqrt {29}} \gt$
Since $v$ has the same direction as $u$ and since it is a multiple of a unit vector $n$, we can write it as: $\overrightarrow{v} = < 2 n, 5n>$ To find the unit vector, we must first find the magnitude: $\sqrt {((2n)^{2} + (5n)^{2}} = 3$ or, $144 \ n^2+25 \ n^2 =9$ This implies that $n^2=\dfrac{ 81}{29} \implies n=\dfrac{9}{\sqrt {29}}$ Now, $\overrightarrow{v} = < 2 (\dfrac{9}{\sqrt {29}}), 5 (\dfrac{9}{\sqrt {29}})> = \lt \dfrac {18}{\sqrt {29}}, \dfrac{ 45}{\sqrt {29}} \gt$
user
The passage describes a mathematical problem involving vector calculations and the determination of a unit vector. It provides a step-by-step solution to find the components of the vector.

TYPE: SINGLE_QUESTION_WITH_ANSWER