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# The vector $\overrightarrow{a}$ and $\overrightarrow{b}$ are not perpendicular and $\overrightarrow{c}$ and $\overrightarrow{d}$ are two vectors satisfying : $\overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{b} \times \overrightarrow{d}$ and $\overrightarrow{a}.\overrightarrow{d} =0$. Then the vector $\overrightarrow{d}$ is equal to

( A ) $\overrightarrow{c} - \begin{pmatrix}\frac{\overrightarrow{a}. \overrightarrow{c}}{\overrightarrow{a}.\overrightarrow{b}} \end{pmatrix} \overrightarrow{b}$
( B ) $\overrightarrow{b} + \begin{pmatrix}\frac{\overrightarrow{b}. \overrightarrow{c}}{\overrightarrow{a}.\overrightarrow{b}} \end{pmatrix} \overrightarrow{b}$
( C ) $\overrightarrow{b} - \begin{pmatrix}\frac{\overrightarrow{b}. \overrightarrow{c}}{\overrightarrow{a}.\overrightarrow{b}} \end{pmatrix} \overrightarrow{b}$
( D ) $\overrightarrow{c} + \begin{pmatrix}\frac{\overrightarrow{a}. \overrightarrow{c}}{\overrightarrow{a}.\overrightarrow{b}} \end{pmatrix} \overrightarrow{b}$