Question

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`?

Answer 1

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.