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

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Answer 1 · 2015-12-14T07:02:25

#=[13, 26, 13]#

The rule for cross products states that for two vectors, #vec a = [a_1, a_2, a_3]# and #vec b = [b_1, b_2, b_3]#;

#vec a xx vec b = [ a_2b_3-a_3b_2, a_3b_1 - b_3a_1, a_1b_2-a_2b_1 ]#

For the two vectors given, this means that;

#[4, ~3, 2] xx [3, 1, ~5] #

#= [(~3)(~5)-(2)(1), (2)(3) - (~5)(4), (4)(1)-(~3)(3) ]#

#=[15-2, 6+20, 4+9]#

#=[13, 26, 13]#