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

1. A
   $\vec{c}+\left(\frac{\vec{a}\cdot \vec{c}}{\vec{a}\cdot \vec{b}}\right)\vec{b}$
2. B
   $\vec{b}+\left(\frac{\vec{b}\cdot \vec{c}}{\vec{a}\cdot \vec{b}}\right)\vec{c}$
3. C
   $\vec{c}-\left(\frac{\vec{a}\cdot \vec{c}}{\vec{a}\cdot \vec{b}}\right)\vec{b}$
4. D
   $\vec{b}-\left(\frac{\vec{b}\cdot \vec{c}}{\vec{a}\cdot \vec{b}}\right)\vec{c}$