Question

The vectors $\vec A$ and $\vec B$ are such that: $|\vec A+\vec B| = |\vec A-\vec B|$. The angle between the two vectors is:

• A. 90°
• B. 60°
• C. 30°
• D. 0°

Answer 1

Answer: (A)

90°

Answer 2

Assume that the angle between A and B is θ
The resultant of |A+B| is given by:
$R =\sqrt {A^2 + B^2 + 2AB\ COS\ θ}$
The resultant of |A-B| is given by:
$R' =\sqrt {A^2 + B^2 - 2AB\ COS\ θ}$
According to question:
$R' = R$
$\sqrt {A^2 + B^2 + 2AB\ COS\ θ}$ = $\sqrt {A^2 + B^2 - 2AB\ COS\ θ}$
⇒ $4AB\ COS\ θ = 0$
⇒ $cos\ θ = 0$,
⇒ $θ = 90°$
So, the correct option is (A): $90°$