What is the norm of $< - 5, 4, 5 >$ $< -5 , 4 , 5 >$ ?

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Answer 1 · 2018-04-10T12:46:19

$\sqrt{66}$ $sqrt 66$

The standard (Euclidean) norm of a vector $\to a = (a_{1}, a_{2}, a_{3})$ $vec a = (a_1,a_2,a_3)$ is

$∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ = \sqrt{a_{1}^{2} + a_{2}^{2} + a_{3}^{2}}$ $||vec a|| =sqrt(a_1^2+a_2^2+a_3^2)$

So, for the given vector, the norm is

$\sqrt{{(- 5)}^{2} + 4^{2} + 5^{2}} = \sqrt{66}$ $sqrt((-5)^2+4^2+5^2) = sqrt 66$

What is the norm of <−5,4,5>< -5 , 4 , 5 >?