What is the cross product of #[1, -2, -3]# and #[2, -5, 8] #?

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Answer 1 · 2016-12-07T17:43:31

The answer is #=〈-31,-14,-1〉#

The cross product of 2 vectors

#veca=〈a_1,a_2,a_3〉#

and #vecb=〈b_1,b_2b_3〉#

is given by

the determinant # | (hati,hatj,hatk), (a_1,a_2,a_3), (b_1,b_2,b_3) | #

#=hati(a_2b_3-a_3b_2)-hatj(a_1b_3-a_3b_1)+hatk(a_1b_2-a_2b_1)#

Here we have,

#〈1.-2-3〉# and #〈2,-5,8〉#

So, the cross product is

# | (hati,hatj,hatk), (1,-2,-3), (2,-5,8) | #

#=hati(-16-15)-hatj(8+6)+hatk(-5+4)#

#=〈-31,-14,-1〉#

Verification (the dot product of perpendicular vectors is #=0#)

#〈-31,-14,-1〉.〈1.-2-3〉=-31+28+3=0#

#〈-31,-14,-1〉.〈2,-5,8〉=-62+70-8=0#