How do you normalize $(- 3 i + 12 j - k)$ $(- 3 i + 12j -k)$ ?

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Answer 1 · 2018-03-14T03:23:31

$\frac{1}{\sqrt{154}} (- 3 ˆ i + 12 ˆ j - ˆ k)$ $1/sqrt(154)(-3\hati + 12\hatj - \hatk)$

You have to calculate the square root of the sum of squares (magnitude) of the vector:

$\sqrt{{(- 3)}^{2} + {(12)}^{2} + {(- 1)}^{2}} = \sqrt{9 + 144 + 1} = \sqrt{154}$ $sqrt((-3)^2+(12)^2+(-1)^2) = sqrt(9+144+1) = sqrt(154)$

Now you simply divide the entire vector by this quantity to normalize:

$\frac{1}{\sqrt{154}} (- 3 ˆ i + 12 ˆ j - ˆ k)$ $1/sqrt(154)(-3\hati + 12\hatj - \hatk)$

How do you normalize (−3i+12j−k)(- 3 i + 12j -k)?