Question
If |𝐴⃗ + 𝐵⃗|^2 = A^2 + B^2 , then: A) 𝐴⃗ and 𝐵⃗ must be parallel and in the same direction
If |𝐴⃗ + 𝐵⃗|^2 = A^2 + B^2 , then:
A) 𝐴⃗ and 𝐵⃗ must be parallel and in the same direction
B) 𝐴⃗ and 𝐵⃗ must be parallel and in opposite directions
C) it must be true that either 𝐴⃗ or 𝐵⃗ is zero
D) the angle between 𝐴⃗ and 𝐵⃗ must be 60
E) none of the above is true
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E) none of the above is true
The given equation can be expanded as |𝐴⃗|^2 + 2(𝐴⃗ ⋅ 𝐵⃗) + |𝐵⃗|^2 = A^2 + B^2
This means that the dot product of 𝐴⃗ and 𝐵⃗, 2(𝐴⃗ ⋅ 𝐵⃗), is not necessarily zero. So 𝐴⃗ and 𝐵⃗ do not need to be parallel or perpendicular, and none of the other options necessarily hold true.
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