What is the cross product of #[3,2, 5]# and #[1,2,-4] #?

1 Answer
Narad T.
Oct 27, 2016

The cross product is #=〈-18,17,4〉#

Explanation:

Let the vectors be #veca=〈a_1,a_2,a_3〉# and #vecb=〈b_1,b_2,b_3〉#

The cross product is given by
#veci##color(white)(aaaa)##vecj##color(white)(aaaa)##veck#
#a_1##color(white)(aaaaa)##a_2##color(white)(aaaa)##a_3#
#b_1##color(white)(aaaaa)##b_2##color(white)(aaaa)##b_3#

#=〈a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1〉#

With the vectors #〈3,2,5〉# and #〈1,2,-4〉#
we get the cross product #〈-8-10,12+5,6-2〉#
#=〈-18,17,4〉#

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