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# Three vectors $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$ satisfy the relation $\overrightarrow{A}.\overrightarrow{B}= 0$ and $\overrightarrow{A}.\overrightarrow{C}=0$ Vector $\overrightarrow{A}$ is parallel to

$\begin{array}{1 1}(A)\;\overrightarrow{B} \\(B)\;\overrightarrow{C} \\(C)\;\overrightarrow{B}.\overrightarrow{C} \\(D)\;\overrightarrow{B} \times \overrightarrow{C} \end{array}$

Since $\overrightarrow{A}.\overrightarrow{B}=0$ So, $\overrightarrow{A} \perp \overrightarrow{B}$.
Also, $\overrightarrow{A}.\overrightarrow{C}=0$ ,So $\overrightarrow{A} \perp \overrightarrow{C}$.
Hence $\overrightarrow{A}$ is normal to the plane containing $\overrightarrow{B}$ and $\overrightarrow{C}$ .
Since $\overrightarrow{B} \times \overrightarrow{C})$ represents a vector normal to the plane containing $\overrightarrow{B}$ and $\overrightarrow{C}$ So $\overrightarrow{A}$ is parallel to $(\overrightarrow{B} \times \overrightarrow{C})$.
Hence D is the correct answer.

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