Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle $$\theta$$, with the vector $$\overrightarrow a $$ + $$\overrightarrow b $$ + $$\overrightarrow c $$. Then 36cos²2$$\theta$$ is equal to ___________.

Let $$A = \left( {\matrix{ 1 & { - 1} & 0 \cr 0 & 1 & { - 1} \cr 0 & 0 & 1 \cr } } \right)$$ and B = 7A²⁰ $$-$$ 20A⁷ + 2I, where I is an identity matrix of order 3 $$\times$$ 3. If B = [b_ij], then b₁₃is equal to _____________.

The number of rational terms in the binomial expansion of $${\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120}}$$ is _______________.

If the shortest distance between the lines $$\overrightarrow {{r_1}} = \alpha \widehat i + 2\widehat j + 2\widehat k + \lambda (\widehat i - 2\widehat j + 2\widehat k)$$, $$\lambda$$ $$\in$$ R, $$\alpha$$ > 0 and $$\overrightarrow {{r_2}} = - 4\widehat i - \widehat k + \mu (3\widehat i - 2\widehat j - 2\widehat k)$$, $$\mu$$ $$\in$$ R is 9, then $$\alpha$$ is equal to ____________.