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 the dipole at $\vec{r} = + \hat{i} + 3 \hat{j} + 5 \hat{k}$ is parallel to:

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

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

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

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

answer is D.

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Detailed Solution

$\begin{array}{l} \vec{r} . \vec{p} = (+ \hat{i} + 3 \hat{j} + 5 \hat{k}) . ((- \hat{i} - 3 \hat{j} + 2 \hat{k}) \times 10^{- 29}) = 0 \\ S o, \vec{r} a n d \vec{p} a r e p e r p e n d i c u l a r t o e a c h o t h e r . \\ H e n c e, t h e p o i n t i s o n p e r p e n d i c u l a r b i s e c t o r o f d i p o l e, w h e r e \vec{E} i s a n t i p a r a l l e l t o \vec{P} . \\ ∴ \vec{E} i s a l o n g (+ \hat{i} + 3 \hat{j} - 2 \hat{k}) \end{array}$