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15 Find a unit vector in the direction of 15 17 A unit vector in the direction of the given vector is 17 (Type an exact answer, using radicals as needed.)

15 Find a unit vector in the direction of 15 17 A unit vector in the direction of the given vector is 17 (Type an exact answer, using radicals as needed.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 47E
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### Finding a Unit Vector To find a unit vector in the direction of a given vector, follow these steps: 1. **Determine the components of the given vector**: \[ \begin{pmatrix} 15 \\ 8 \\ 1 \end{pmatrix} \] 2. **Normalize the vector**: To find a unit vector, divide each component of the given vector by its magnitude. 3. **Magnitude Calculation**: The magnitude of the vector is determined by: \[ \sqrt{15^2 + 8^2 + 1^2} = \sqrt{225 + 64 + 1} = \sqrt{290} \] 4. **Unit Vector**: Divide each component by the magnitude: \[ \frac{1}{\sqrt{290}} \begin{pmatrix} 15 \\ 8 \\ 1 \end{pmatrix} = \begin{pmatrix} \frac{15}{\sqrt{290}} \\ \frac{8}{\sqrt{290}} \\ \frac{1}{\sqrt{290}} \end{pmatrix} \] ### Problem Statement Breakdown: The interface displays: 1. **Problem Prompt**: \[ \text{Find a unit vector in the direction of} \ \begin{pmatrix} 15 \\ 8 \\ 1 \end{pmatrix} \] 2. **Solution Suggestion**: \[ \text{A unit vector in the direction of the given vector is} \ \begin{pmatrix} \frac{15}{\sqrt{290}} \\ \frac{8}{\sqrt{290}} \\ \frac{1}{\sqrt{290}} \end{pmatrix} \] 3. **Input Instructions**: \[ \text{Type an exact answer, using radicals as needed.} \] 4. **Action Prompt**: \[ \text{Enter your answer in the answer box and then click Check Answer.} \] 5. **UI Elements**: - A button labeled "Clear All" to reset the input. - A progress bar indicating completion status with
Transcribed Image Text:### Finding a Unit Vector To find a unit vector in the direction of a given vector, follow these steps: 1. **Determine the components of the given vector**: \[ \begin{pmatrix} 15 \\ 8 \\ 1 \end{pmatrix} \] 2. **Normalize the vector**: To find a unit vector, divide each component of the given vector by its magnitude. 3. **Magnitude Calculation**: The magnitude of the vector is determined by: \[ \sqrt{15^2 + 8^2 + 1^2} = \sqrt{225 + 64 + 1} = \sqrt{290} \] 4. **Unit Vector**: Divide each component by the magnitude: \[ \frac{1}{\sqrt{290}} \begin{pmatrix} 15 \\ 8 \\ 1 \end{pmatrix} = \begin{pmatrix} \frac{15}{\sqrt{290}} \\ \frac{8}{\sqrt{290}} \\ \frac{1}{\sqrt{290}} \end{pmatrix} \] ### Problem Statement Breakdown: The interface displays: 1. **Problem Prompt**: \[ \text{Find a unit vector in the direction of} \ \begin{pmatrix} 15 \\ 8 \\ 1 \end{pmatrix} \] 2. **Solution Suggestion**: \[ \text{A unit vector in the direction of the given vector is} \ \begin{pmatrix} \frac{15}{\sqrt{290}} \\ \frac{8}{\sqrt{290}} \\ \frac{1}{\sqrt{290}} \end{pmatrix} \] 3. **Input Instructions**: \[ \text{Type an exact answer, using radicals as needed.} \] 4. **Action Prompt**: \[ \text{Enter your answer in the answer box and then click Check Answer.} \] 5. **UI Elements**: - A button labeled "Clear All" to reset the input. - A progress bar indicating completion status with
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