If $\cot ^{-1}(7)+\cot ^{-1}(8)+\cot ^{-1}(18)=\cot ^{-1} x$, then the value of $x$ is

If $\mathrm{P}(\mathrm{X}=2)=0.3, \mathrm{P}(\mathrm{X}=3)=0.4, \mathrm{P}(\mathrm{X}=4)=0.3$, then the variance of random variable X is

The Cartesian equation of a line is $2 x-2=3 y+1=6 z-2$, then the vector equation of the line is

Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$. Let $\overline{\mathrm{c}}$ be a vector such that $|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=3$ and $|(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}|=3$ and the angle between $\bar{c}$ and $\bar{a} \times \bar{b}$ is $30^{\circ}$, then $\bar{a} \cdot \bar{c}$ is equal to