The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle $$\alpha$$. The equation changes to

The equation of the plane through the point $$(2, - 1, - 3)$$ and parallel to the lines

$${{x - 1} \over 2} = {{y + 2} \over 3} = {z \over { - 4}}$$ and $${x \over 2} = {{y - 1} \over { - 3}} = {{z - 2} \over 2}$$ is

The sine of the angle between the straight line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ and the plane $$2x - 2y + z = 5$$ is

The direction ratios of the normal to the plane passing through the points (1, 2, $$-$$3), ($$-$$1, $$-$$2, 1) and parallel to $${{x - 2} \over 2} = {{y + 1} \over 3} = {z \over 4}$$ is