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Find the magnitude of the vector \( <5,-3> \) \( \begin{array}{l}4 \\ 5.8 \\ 6.1 \\ 5.2\end{array} \)

Ask by Young Rodriguez. in the United States
Feb 26,2025

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The magnitude of the vector <5, -3> is approximately 5.8.

Solución

To find the magnitude of the vector <5, -3>, use the formula for the magnitude of a vector in two dimensions:   Magnitude = √(x² + y²) For the vector <5, -3>:   Magnitude = √(5² + (-3)²)        = √(25 + 9)        = √34 The approximate value of √34 is about 5.8. Therefore, the correct answer from the choices provided is 5.8.

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The Deep Dive

To find the magnitude of the vector \( <5, -3> \), you can use the formula for the magnitude of a vector, which is given by: \[ \text{Magnitude} = \sqrt{x^2 + y^2} \] For the vector \( <5, -3> \): \[ \text{Magnitude} = \sqrt{5^2 + (-3)^2} = \sqrt{25 + 9} = \sqrt{34} \approx 5.83 \] So, the closest option from your list is \( 5.8 \).

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