Let [t] denote the greatest integer less than or equal to t.
Then the value of $$\int\limits_1^2 {\left| {2x - \left[ {3x} \right]} \right|dx} $$ is ______.

Let the position vectors of points 'A' and 'B' be
$$\widehat i + \widehat j + \widehat k$$ and $$2\widehat i + \widehat j + 3\widehat k$$, respectively. A point 'P' divides the line segment AB internally in the ratio $$\lambda $$ : 1 ( $$\lambda $$ > 0). If O is the origin and
$$\overrightarrow {OB} .\overrightarrow {OP} - 3{\left| {\overrightarrow {OA} \times \overrightarrow {OP} } \right|^2} = 6$$, then $$\lambda $$ is equal to______.

For a positive integer n,
$${\left( {1 + {1 \over x}} \right)^n}$$ is expanded
in increasing powers of x. If three consecutive
coefficients in this expansion are in the ratio,
2 : 5 : 12, then n is equal to________.

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by $$\widehat k$$ and $$2\widehat i - 2\widehat j$$, respectively. What is the unit vector along direction of propagation of the wave?