Question

If for two vector $\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$, sum $(\overset{\rightarrow}{A} + \overset{\rightarrow}{B})$ is perpendicular to the difference $(\overset{\rightarrow}{A} - \overset{\rightarrow}{B})$. The ratio of their magnitude is

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

Answer: (A)

1

Answer 2

$(\overset{\rightarrow}{A} + \overset{\rightarrow}{B})$ is perpendicular to $(\overset{\rightarrow}{A} - \overset{\rightarrow}{B})$. Thus

$(\overset{\rightarrow}{A} + \overset{\rightarrow}{B})$.$(\overset{\rightarrow}{A} - \overset{\rightarrow}{B})$ = 0

or $A^{2} + \overset{\rightarrow}{B} ⥂ .\overset{\rightarrow}{A} - \overset{\rightarrow}{A}.\overset{\rightarrow}{B} - B^{2} = 0$

Because of commutative property of dot product $\overset{\rightarrow}{A}.\overset{\rightarrow}{B} = \overset{\rightarrow}{B}.\overset{\rightarrow}{A}$

$\therefore$ $A^{2} - B^{2} = 0$ or $A = B$

Thus the ratio of magnitudes A/B = 1