How do you normalize $< 0, 4, 4 >$ $<0, 4, 4>$ ?

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How do you normalize $< 0, 4, 4 >$ $<0, 4, 4>$ ?

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Answer 1 · 2017-03-26T13:53:58

The normalized vector is

$\frac{v}{| v |}$ $v/|v|$

where $| v | = \sqrt{u_{x}^{2} + u_{y}^{2} + u_{z}^{2}}$ $|v|=sqrt(u_x^2+u_y^2+u_z^2)$

hence $| v | = \sqrt{0^{2} + 4^{2} + 4^{2}}$ $|v|=sqrt(0^2+4^2+4^2)$ or $| v | = 4 \cdot \sqrt{2}$ $|v|=4*sqrt2$

Hence

$\frac{v}{| v |} = (\frac{0}{4 \cdot \sqrt{2}}, \frac{4}{4 \cdot \sqrt{2}}, \frac{4}{4 \cdot \sqrt{2}})$ $v/|v|=(0/(4*sqrt2) , 4/[4*sqrt2],4/[4*sqrt2])$

$\frac{v}{| v |} = (0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$ $v/|v|=(0,1/sqrt2,1/sqrt2)$

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How do you normalize $< 0, 4, 4 >$ $<0, 4, 4>$ ?

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