What is the value of #(A #x# B)^2# + #(A * B)^2# ?

Question

Please interpret this as the sum of the squares of the cross product and dot product of two vectors A and B.
Thanks:)

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Answer 1 · 2016-11-29T13:37:47

#absA^2 absB^2#

#abs(A xx B)=absA absB sinphi#
#abs(A cdot B)=absA absB cos phi#

here #phi# is the angle between #A# and #B# at common tails.

then

#abs(A xx B)^2+abs(A cdot B)^2=absA^2absB^2(sin^2phi+cos^phi) = absA^2absB^2#