How do you normalize $(- 5 i + 4 j - 5 k)$ $( - 5 i + 4 j - 5 k )$ ?

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How do you normalize $(- 5 i + 4 j - 5 k)$ $( - 5 i + 4 j - 5 k )$ ?

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Answer 1 · 2016-12-29T04:35:24

Normalized vector is $- \frac{5}{\sqrt{66}} ˆ i + \frac{4}{\sqrt{66}} ˆ j - \frac{5}{\sqrt{66}} ˆ k$ $-5/sqrt66hati+4/sqrt66hatj-5/sqrt66hatk$

Explanation:

Normalizing a vector $(- 5 ˆ i + 4 ˆ j - 5 ˆ k)$ $(-5hati+4hatj-5hatk)$ means

a unit vector, whose initial point is same but terminal point is one unit in the same direction.

Hence, for a vector $\to v = a ˆ i + b ˆ j + c ˆ k$ $vecv=ahati+bhatj+chatk$ , its normalized vector is $\frac{1}{| v |} (a ˆ i + b ˆ j + c ˆ k)$ $1/|v|(ahati+bhatj+chatk)$ , where $| v | = \sqrt{a^{2} + b^{2} + c^{2}}$ $|v|=sqrt(a^2+b^2+c^2)$

and for $(- 5 ˆ i + 4 ˆ j - 5 ˆ k)$ $(-5hati+4hatj-5hatk)$ , its normalized vector is

$\frac{1}{\sqrt{{(- 5)}^{2} + 4^{2} + {(- 5)}^{2}}} (- 5 ˆ i + 4 ˆ j - 5 ˆ k)$ $1/sqrt((-5)^2+4^2+(-5)^2)(-5hati+4hatj-5hatk)$

= $\frac{1}{\sqrt{25 + 16 + 25}} (- 5 ˆ i + 4 ˆ j - 5 ˆ k)$ $1/sqrt(25+16+25)(-5hati+4hatj-5hatk)$

= $- \frac{5}{\sqrt{66}} ˆ i + \frac{4}{\sqrt{66}} ˆ j - \frac{5}{\sqrt{66}} ˆ k$ $-5/sqrt66hati+4/sqrt66hatj-5/sqrt66hatk$

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How do you normalize $(- 5 i + 4 j - 5 k)$ $( - 5 i + 4 j - 5 k )$ ?

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How do you normalize ( - 5 i + 4 j - 5 k )(−5i+4j−5k)( - 5 i + 4 j - 5 k )?

1 Answer

Explanation:

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How do you normalize $(- 5 i + 4 j - 5 k)$ $( - 5 i + 4 j - 5 k )$ ?