Cross product calculator calculates the cross product of two vectors a and b in three-dimensional space. Enter i, j, and k for both vectors to get the resultant vector c.

c = a × b

This vector cross product calculator shows step by steps vector multiplication.

## What is cross product?

Cross product is a multiplication of two vectors in three-dimensional space. It is denoted by the symbol ‘×’.  Cross product of two vectors a and b is a vector that is perpendicular to both a and b.

Note: Read a × b as a cross b. Image credit: “Cross Products” by Khan Academy.

## Cross product formula

Below equation is used to find the cross product of two vectors.

a × b = |a| |b| sin(θ) n

In this equation:

|a| is length of vector a

|b| is length of vector b

θ is the angle between a and b

n is the unit vector perpendicular to a and b.

We can also calculate cross product by using the coordinate points of both vectors.

(ai aj ak) × (bi bj bk) = (aj × bk - ak × bj    ak × bi - ai × bk    ai  bj - aj × bi)

Where

i, j, and k represents x, y, and z coordinates on Cartesian plane.

References:
{"ft_lang_label":"__label__en","ft_lang_prob":0.908486,"math_prob":0.9963712,"size":1121,"snap":"2022-27-2022-33","text_gpt3_token_len":279,"char_repetition_ratio":0.18531781,"word_repetition_ratio":0.03652968,"special_character_ratio":0.2542373,"punctuation_ratio":0.10638298,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99982387,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-12T23:31:17Z\",\"WARC-Record-ID\":\"<urn:uuid:4c738982-71e3-4ea4-875e-d149f76e66c8>\",\"Content-Length\":\"10670\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:36f75d69-bdc9-44cc-9785-3ba6edb5147c>\",\"WARC-Concurrent-To\":\"<urn:uuid:e1b6563b-be07-4479-a0cb-40e427667524>\",\"WARC-IP-Address\":\"162.0.215.212\",\"WARC-Target-URI\":\"https://crossproductcalculator.tech/index.html\",\"WARC-Payload-Digest\":\"sha1:75VVCIH4PGPTPW2QL45OEBLPPKQSZ25I\",\"WARC-Block-Digest\":\"sha1:FO4LXORJFO2SEKMMNZROJVULBKR6GT56\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571847.45_warc_CC-MAIN-20220812230927-20220813020927-00275.warc.gz\"}"}