The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $$-$$ n = 0 and mn + nl + lm = 0, is :

The equation of the plane passing through the line of intersection of the planes $$\overrightarrow r .\left( {\widehat i + \widehat j + \widehat k} \right) = 1$$ and $$\overrightarrow r .\left( {2\widehat i + 3\widehat j - \widehat k} \right) + 4 = 0$$ and parallel to the x-axis is :

The distance of the point (1, $$-$$2, 3) from the plane x $$-$$ y + z = 5 measured parallel to a line, whose direction ratios are 2, 3, $$-$$6 is :

Equation of a plane at a distance $$\sqrt {{2 \over {21}}} $$ from the origin, which contains the line of intersection of the planes x $$-$$ y $$-$$ z $$-$$ 1 = 0 and 2x + y $$-$$ 3z + 4 = 0, is :