An electric dipole of moment

Question:

An electric dipole of moment $\vec{p}=(\hat{i}-3 \hat{j}+2 \hat{k}) \times 10^{-29}$ C.m is at the origin $(0,0,0)$. The electric field due to this dipole at $\vec{r}=+\hat{i}+3 \hat{j}+5 \hat{k}$

(note that $\vec{r} \cdot \vec{p}=0$ ) is parallel to:

1. (1) $(+\hat{i}-3 \hat{j}-2 \hat{k})$

2. (2) $(-\hat{i}+3 \hat{j}-2 \hat{k})$

3. (3) $(+\hat{i}+3 \hat{j}-2 \hat{k})$

4. (4) $(-\hat{i}-3 \hat{j}+2 \hat{k})$

Correct Option: , 3

Solution:

(3) Since $\vec{r} \cdot \vec{p}=0$

$\vec{E}$ must be antiparallel to $\vec{p}$

$\therefore \hat{E}$ is parallel to $(\hat{i}+3 \hat{j}-2 \hat{k})$