Question

Given v = (-3, 4), what is ||3v|?

Answer 1

9514 1404 393

Answer:

  15

Step-by-step explanation:

||3v|| = ||(-9, 12)|| = √((-9)² +12²) = √225

||3v|| = 15

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Additional comment

The (3, 4, 5) Pythagorean triple shows up in numerous algebra, geometry, and trigonometry problems. This is one of them. Once you identify the magnitude of v as the hypotenuse of a triangle with legs 3 and 4, you know immediately that ||v|| = 5 and ||3v|| = 15.