Question

If for two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$, sum $(\overrightarrow{A}+\overrightarrow{b})$ is perpendicular to the difference $(\overrightarrow{A}-\overrightarrow{B})$

Find the ratio of the magnitude $\left(\frac{A}{B}\right)$.

• A. 1
• B. 2
• C. 0.5
• D. 1.25

Answer 1

The correct option is A

1

$(\overrightarrow{A}+\overrightarrow{B})$ is perpendicular to $(\overrightarrow{A}-\overrightarrow{B})$Thus

$(\overrightarrow{A}+\overrightarrow{B})$.$(\overrightarrow{A}+\overrightarrow{B})$= 0 or $A^2+\overrightarrow{B}.\overrightarrow{A}-B^2=0$ Because of commutative property of dot product

$\overrightarrow{A}.\overrightarrow{B}=\overrightarrow{B}.\overrightarrow{A}$

$\therefore A^2-B^2=0$ or A = B (as A, Thus the ratio of magnitudes $\frac{A}{B}$ = 1