How do you normalize $(i + 2 j + 2 k)$ $(i+2j+2k)$ ?

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Answer 1 · 2018-07-26T14:31:10

The answer is $= < \frac{1}{3}, \frac{2}{3}, \frac{2}{3} >$ $=<1/3,2/3,2/3>$

To normalize a vector $\to a$ $veca$ , calculate

$ˆ a = \frac{\to a}{∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣}$ $hata=veca/(||veca||)$

Here,

$\to a = < 1, 2, 2 >$ $veca = <1,2,2>$

The norm is

$∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ = | | < 1, 2, 2 > | | = \sqrt{1^{2} + 2^{2} + 2^{2}}$ $||veca ||= ||<1,2,2>|| = sqrt(1^2+2^2+2^2)$

$= \sqrt{1 + 4 + 4}$ $=sqrt(1+4+4)$

$= \sqrt{9}$ $=sqrt9$

$= 3$ $=3$

Therefore,

$ˆ a = \frac{1}{3} < 1, 2, 2 > = < \frac{1}{3}, \frac{2}{3}, \frac{2}{3} >$ $hata=1/3 <1,2,2> = <1/3,2/3,2/3>$

How do you normalize (i+2j+2k)(i+2j+2k)?