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# Practice Active Given $\vec{\pi}=\{4,- 1\}$ and $\vec{\nu}=\{3,3\}$, find the magnitude of $\vec{\mu}+ 2 \vec{\pi}$. A. $2 \sqrt{3}$ B. 11 C. $\sqrt{122}$ D. 122 Please select the best answer from the choices provided O A O B O C O D
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Answer

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Step 1:
: First, find the vector addition of $\vec{\mu}$ and $2\vec{\pi}$.

\vec{\mu} + 2\vec{\pi} = \{4,-1\} + 2\{3,3\}
To do this, add the corresponding components of the vectors.

Step 2:
: This simplifies to:

\vec{\mu} + 2\vec{\pi} = \{4,-1\} + \{6,6\}

Step 3:
: Now, perform the addition:

\vec{\mu} + 2\vec{\pi} = \{4+6,-1+6\} = \{10,5\}

Step 4:
: To find the magnitude of the resulting vector, use the formula:

|\vec{v}| = \sqrt{v\_x^2 + v\_y^2}

Step 5:
: Plug in the values from the resulting vector:

|\vec{\mu} + 2\vec{\pi}| = \sqrt{10^2 + 5^2}

Step 6:
: Calculate the result:

|\vec{\mu} + 2\vec{\pi}| = \sqrt{100 + 25} = \sqrt{125}

Step 7:
: Simplify the result:

5\sqrt{5} \approx 11.18
Since the closest answer choice is 11, the answer could be:

Final Answer

B. 11 (with the understanding that this is an approximation)