If bb(ul(A)) = A_1 bb(ul(hat i)) + A_2 bb(ul(hat j)) + A_3 bb(ul(hat k)) does abs(bb(ul(A))) = A_1 + A_2 + A_3 ?

1 Answer
Steve M
Sep 25, 2017

If

bb(ul(A)) = A_1 bb(ul(hat i)) + A_2 bb(ul(hat j)) + A_3 bb(ul(hat k))

Then, its magnitude, is:

abs(bb(ul(A))) = sqrt( bb(ul(A)) * bb(ul(A))
\ \ \ \ \ = sqrt( A_1A_1 + A_2A_2 + A_3A_3 )
\ \ \ \ \ = sqrt( A_1^2 + A_2^2 + A_3^2 )
\ \ \ \ \ != A_1 + A_2 + A_3

Proving that the given result is invalid.

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