Let $$P$$ be the plane such that it contains the straight line $$\dfrac{x-1}{2}=\dfrac{y-3}{3}=\dfrac{z+2}{1}$$ and is perpendicular to the plane $$x+2y+3z=4$$. Let $$P_1$$ be the plane which passes through the point $$(4,2,2)$$ and is parallel to $$P$$.

Then which of the following statements is (are) TRUE?

A

The equation of the plane $$P$$ is $$7x-5y+z=-10$$

B

The distance between the planes $$P$$ and $$P_1$$ is $$30$$

C

The distance of the plane $$P$$ from the origin is $$2\sqrt{3}$$

D

The acute angle between the plane $$P$$ and the plane $$2x+2y+z=3$$ is $$\cos^{-1}\!\left(\tfrac{1}{3\sqrt{3}}\right)$$