Robbins Best
06/05/2024 · Elementary School
Calcula la norma del vector \[ \begin{array}{l}\text { a) } U=(3,-4) \\ \text { b) } U=(3,4) \\ \text { c) } U=(4,7) \\ \text { d) } U=(3,7 / 6)\end{array} \]
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Tutor-Verified Answer
Step-by-step Solution
La norma de un vector \( U = (x, y) \) se calcula utilizando la fórmula:
\[
\| U \| = \sqrt{x^2 + y^2}
\]
Ahora, calcularemos la norma para cada uno de los vectores dados:
a) Para \( U = (3, -4) \):
\[
\| U \| = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]
b) Para \( U = (3, 4) \):
\[
\| U \| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]
c) Para \( U = (4, 7) \):
\[
\| U \| = \sqrt{4^2 + 7^2} = \sqrt{16 + 49} = \sqrt{65}
\]
d) Para \( U = \left(3, \frac{7}{6}\right) \):
\[
\| U \| = \sqrt{3^2 + \left(\frac{7}{6}\right)^2} = \sqrt{9 + \frac{49}{36}} = \sqrt{\frac{324}{36} + \frac{49}{36}} = \sqrt{\frac{373}{36}} = \frac{\sqrt{373}}{6}
\]
Resumiendo los resultados:
- a) \( \| U \| = 5 \)
- b) \( \| U \| = 5 \)
- c) \( \| U \| = \sqrt{65} \)
- d) \( \| U \| = \frac{\sqrt{373}}{6} \)
Quick Answer
- a) \( \| U \| = 5 \)
- b) \( \| U \| = 5 \)
- c) \( \| U \| = \sqrt{65} \)
- d) \( \| U \| = \frac{\sqrt{373}}{6} \)
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