Vectors A + B: Are Any of the Above True?

[Ryan McCormick]

Homework Statement

If magnitude (absolute value) of vectors ( A + B ) ^2 = A^2 + B^2 then:
a) A and B must be parallel and in the same direction
b) A and B must be parallel and in opposite directions
c) it must be true that either A or B is zero
d) the angle between A and B must be 60 degrees
e) None of the above

I thought the answer was (c) just by foiling out the left side of the equation. but the answer is (e) none of the above, and I'd like an explanation as to why (c) is not correct.

 

[Qwertywerty]

How, exactly, did you proceed? Could you elaborate?

 

[Ryan McCormick]

After foiling the left side of the equation you get, A^2 + 2AB + B^2 = A^2 + B^2 so in order for that to be true, the middle term (2AB) must be zero which means either A, B, or both must be 0. Unless you're not allowed to foil out the equation in this scenario for some reason, I don't understand why my reasoning isn't correct.

 

[Qwertywerty]

Are A and B vectors? If so, considering an angle θ between them, is your formula for (A+B)² valid?

 

[Charles Link]

For a vector V=A+B, V^2=V*V where "*" is a dot product. ==>> (A+B)^2=A^2+2A*B +B^2 where A*B is a dot product. Thereby A*B=0 is the result you need, but that can be zero if A is zero, or B is zero, or if A is perpendicular to B.