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

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

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Answer 1 · 2016-01-03T21:25:39

Divide by the scalar $| i + k | = \sqrt{2}$ $abs(i+k) = sqrt(2)$ to get:

$\frac{\sqrt{2}}{2} i + \frac{\sqrt{2}}{2} k$ $sqrt(2)/2 i + sqrt(2)/2 k$

Explanation:

$| i + k | = \sqrt{1^{2} + 1^{2}} = \sqrt{2}$ $abs(i+k) = sqrt(1^2+1^2) = sqrt(2)$

So multiplying by $\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ $1/sqrt(2) = sqrt(2)/2$ we find:

$∣ ∣ ∣ \frac{\sqrt{2}}{2} i + \frac{\sqrt{2}}{2} k ∣ ∣ ∣ = \sqrt{{(\frac{\sqrt{2}}{2})}^{2} + {(\frac{\sqrt{2}}{2})}^{2}}$ $abs(sqrt(2)/2 i + sqrt(2)/2 k) = sqrt((sqrt(2)/2)^2 + (sqrt(2)/2)^2)$

$= \sqrt{\frac{1}{2} + \frac{1}{2}} = \sqrt{1} = 1$ $= sqrt(1/2+1/2) = sqrt(1) = 1$

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