What is the cross product of #[1, 4, -2]# and #[3, 0, 5] #?

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Answer 1 · 2017-01-18T15:41:33

#20hatveci-11hatvecj-12hatveck#

the cross product of two vectors

#veca=[a_1,a_2,a_3]# and #vecb=[b_1,b_2,b_3]#

is calculated by the determinate

#vecaxxvecb=|(hatveci,hatvecj,hatveck),(a_1,a_2,a_3),(b_1,b_2,b_3)|#

so we have here

#vecaxxvecb=|(hatveci,hatvecj,hatveck),(1,4,-2),(3,0,5)|#

expanding by Row 1

#=hatveci|(4,-2),(0,5)|-hatvecj|(1,-2),(3,5)|+hatveck|(1,4),(3,0)|#

#=(4xx5-0xx(-2))hatveci-(1xx5-3xx(-2))hatvecj+(1xx0-4xx3)hatveck#

#=20hatveci-11hatvecj-12hatveck#