Question

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

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

Answer 1

The correct option is A $1$

$(\overrightarrow{A}+\overrightarrow{B})\text{is perpendicular to}(\overrightarrow{A}-\overrightarrow{B})$
Thus $(\overrightarrow{A}+\overrightarrow{B}).(\overrightarrow{A}-\overrightarrow{B})=0$
Commutative property of dot product $\overrightarrow{A}.\overrightarrow{B}=\overrightarrow{B}.\overrightarrow{A}$
$\therefore A^2-B^2=0\text{or}A=\pm B$
Thus the ratio of magnitudes
$\frac{A}{B}=1$ (since , magnitude cannot be negative)