The smaller angle (in degrees) between the planes $$x+y+z=1$$ and $$2x-y+2z=0$$ is ________.

A vector $$\overrightarrow P $$ is given by $$\,\,\overrightarrow P = {x^3}y\overrightarrow a {}_x - {x^2}{y^2}\overrightarrow a {}_y - {x^2}yz\overrightarrow a {}_z.\,\,\,$$ Which one of the following statements is TRUE?

The magnitude of the gradient for the function $$f\left( {x,y,z} \right) = {x^2} + 3{y^2} + {z^3}\,\,$$ at the point $$(1,1,1)$$ is _________.

The directional derivative of $$f\left( {x,y} \right) = {{xy} \over {\sqrt 2 }}\left( {x + y} \right)$$ at $$(1, 1)$$ in the direction of the unit vector at an angle of $${\pi \over 4}$$ with $$y-$$axis, is given by ________.