Question

If $(\overline{A}+\overline{B})$ is perpendicular to$\overline{B}$ and If $(\overline{A}+2\overline{B})$ is perpendicular to $\overline{A}$, then

• A. $A=\sqrt{2}B$
• B. $A=2B$
• C. $2A=B$
• D. $A=B$

Answer 1

The correct option is A $A=\sqrt{2}B$

Given $(\overline{A}+\overline{B})$ is perpendicular to$\overline{B}$
$\Rightarrow (\overline{A}+\overline{B})\cdot \overline{B}=0$
$\Rightarrow \overline{A}\cdot \overline{B}+B^2=0$ -----(1)
And $(\overline{A}+2\overline{B})$ is perpendicular to $\overline{A}$.
$\Rightarrow (\overline{A}+2\overline{B})\cdot \overline{A}=0$
$\Rightarrow A^2+2\overline{A}\cdot \overline{B}=0$ ------(2)
from (1) and (2)
$A^2=2B^2$
$\therefore A=\sqrt{2}B$
Hence, option A.