Question

A point charges $q$ is placed at origin. Let ${\overrightarrow{E}}_A,{\overrightarrow{E}}_B$ and ${\overrightarrow{E}}_C$ be the electric field at three points $A(1,2,3),B(1,1,-1)$ and $C(2,2,2)$ due to charge $q$. Consider the following statement and choose correct alternative.
i) ${\overrightarrow{E}}_A\perp {\overrightarrow{E}}_B$
ii) $|{\overrightarrow{E}}_B|=4|{\overrightarrow{E}}_C|$

• A. only $\left[i\right]$ is correct
• B. only $\left[ii\right]$ is correct
• C. both $\left[ii\right]$ and $\left[ii\right]$ is correct
• D. both $\left[ii\right]$ and $\left[ii\right]$ is wrong

Answer 1

The correct option is A only $\left[i\right]$ is correct

(i) Option (i) is correct because ${\overline{E}}_A\perp {\overline{E}}_B$ for checking of perpendicularity

$\tan \theta =\tan {90}^0=\alpha$

${\tan 45}^0=1$

${\tan }^{-1}\left(\frac{3-2}{1}\right)={\tan }^{-1}\left(1\right)=45$ (for ${\overline{E}}_A$)

and $E_B(1,1,-1)$

$\tan \left(\frac{-1+1}{2}\right)={\tan 0}^0=0$