# How do you normalize  <3,-6,4>?

##### 1 Answer
Mar 4, 2017

$u = < \frac{3}{\sqrt{61}} , - \frac{6}{\sqrt{61}} , \frac{4}{\sqrt{61}} >$

#### Explanation:

In normalizing the vector we are finding a unit vector (magnitude/length of one) in the same direction as the given vector. This can be accomplished by dividing the given vector by its magnitude.

$u = \frac{v}{| v |}$

Given $v = < 3 , - 6 , 4 >$, we can calculate the magnitude of the vector:

$| v | = \sqrt{{\left({v}_{x}\right)}^{2} + {\left({v}_{y}\right)}^{2} + {\left({v}_{z}\right)}^{2}}$

$| v | = \sqrt{{\left(3\right)}^{2} + {\left(- 6\right)}^{2} + {\left(4\right)}^{2}}$

$| v | = \sqrt{9 + 36 + 16}$

$| v | = \sqrt{61}$

We now have:

$u = \frac{< 3 , - 6 , 4 >}{\sqrt{61}}$

$\implies u = < \frac{3}{\sqrt{61}} , - \frac{6}{\sqrt{61}} , \frac{4}{\sqrt{61}} >$

Hope that helps!
{"ft_lang_label":"__label__en","ft_lang_prob":0.6120078,"math_prob":1.0000083,"size":564,"snap":"2021-21-2021-25","text_gpt3_token_len":190,"char_repetition_ratio":0.12678571,"word_repetition_ratio":0.0,"special_character_ratio":0.3617021,"punctuation_ratio":0.09322034,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000056,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-22T17:39:27Z\",\"WARC-Record-ID\":\"<urn:uuid:bf93bd9f-4c42-403c-a683-0aaa06139079>\",\"Content-Length\":\"33357\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3fc1d21e-dbd6-4ec5-9648-bf44b7e1ec92>\",\"WARC-Concurrent-To\":\"<urn:uuid:0fb020f8-22c1-4a21-9013-4110eab9186f>\",\"WARC-IP-Address\":\"216.239.32.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/how-do-you-normalize-3-6-4\",\"WARC-Payload-Digest\":\"sha1:VBXU7EK4Q4OBACJTO25KVOM2SEXNWU6T\",\"WARC-Block-Digest\":\"sha1:TNU3BIRKSQHPXEUF3A6CRV6JZ2RGK6YY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488519183.85_warc_CC-MAIN-20210622155328-20210622185328-00387.warc.gz\"}"}