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

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