How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors #<1,-3,2>times<5,1,-2>#?

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Answer 1 · 2016-11-16T07:21:41

The vector is #=〈4,12,16〉#

The cross product is calculated by the determinant

#vecu.vecv=#

#〈1,-3,2〉#x#〈5,1,-2〉#

#∣ ((i,j,k) , (1,-3,2) , (5,1,-2)) ∣#

#=i(6-2)-j(-2-10)+k(1+15)#

#vecw=〈4,12,16〉#

To verify, we do the dot products

#〈4,12,16〉.〈1,-3,2〉=4-36+32=0#

#〈4,12,16〉.〈5,1,-2〉=20+12-32=0#

Therefore #vecw# is perpendicular to #vecu# and #vecv#