QQuestionMathematics
QuestionMathematics
# 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)
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