Which from following lanthanoids exhibits no effective magnetic moment in +3 state?

The equation of the line passing through the point of intersection of the lines $3 x-y=5$ and $x+3 y=1$ and making equal intercepts on the axes is

$$\int \frac{\operatorname{cosec} x d x}{\cos ^2\left(1+\log \tan \frac{x}{2}\right)}=$$

The vectors $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are not perpendicular and $\overline{\mathrm{c}}$ and $\overline{\mathrm{d}}$ are two vectors satisfying $\overline{\mathrm{b}} \times \overline{\mathrm{c}}=\overline{\mathrm{b}} \times \overline{\mathrm{d}}$ and $\overline{\mathrm{a}} \cdot \overline{\mathrm{d}}=0$, then the vector $\overline{\mathrm{d}}$ is equal to