If ||v|| = 3, what is ||-2v||?

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If ||v|| = 3, what is ||-2v||?

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Answer 1 · 2015-11-06T10:48:50

The norm of $-2v$ is $6$

Explanation:

Using formulas, you know that $||\lambda v|| = |lambda| ||v||$ , so

$||-2v|| = |-2| ||v|| = 2||v|| = 2*3=6$ .

Intuitively, the norm measures the leght of a vector, and multiplying a vector by a number means to stretch (or shrink) the vector according to the number. For example, $2v$ is long two times the leght of $v$ , and $1/3 v$ is long one third of the lenght of $v$ .

The sign of the number only affect the direction of the vector: $5v$ is long five times the original lenght and has the same orientation as $v$ , while $-9v$ is long nine times the lenght of $v$ and has the opposite orientation.

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If ||v|| = 3, what is ||-2v||?

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