Let $\displaystyle \mathbf{\overrightarrow{a} = i + j -2k }$ , $\displaystyle \mathbf{\overrightarrow{b} = 2i + j + k}$ and $\displaystyle \mathbf{\overrightarrow{c} = 4i + j - 2k}$ . Find a vector $\displaystyle \mathbf{\overrightarrow{d}}$ such that $\displaystyle \mathbf{\overrightarrow{d} \times \overrightarrow{b} = \overrightarrow{c} \times \overrightarrow{b}}$ and $\displaystyle \mathbf{\overrightarrow{d} . \overrightarrow{a}}=0$.