What is the cross product of #(- 5 i + 4 j - 5 k)# and #(i + j -7k)#?

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Answer 1 · 2016-07-03T21:01:19

#= -23 hat i -40 hat j -9 hat k#

the cross product is the determinant of this matrix

#[(hat i, hat j,hat k), (-5, 4, -5), (1,1,-7)]#

which is

#hat i [(4)(-7)-(1)(-5)] #

#- hat j [(-5)(-7) - (1)(-5)] #

#+ hat k [(-5)(1) - (1)(4)] #

#= [(-23), (-40), (-9)]#