The length of the perpendicular from the point (2, –1, 4) on the straight line,

$${{x + 3} \over {10}}$$= $${{y - 2} \over {-7}}$$ = $${{z} \over {1}}$$ is :

Let S be the set of all real values of $$\lambda $$ such that a plane passing through the points (–$$\lambda $$², 1, 1), (1, –$$\lambda $$², 1) and (1, 1, – $$\lambda $$²) also passes through the point (–1, –1, 1). Then S is equal to :

If an angle between the line, $${{x + 1} \over 2} = {{y - 2} \over 1} = {{z - 3} \over { - 2}}$$ and the plane, $$x - 2y - kz = 3$$ is $${\cos ^{ - 1}}\left( {{{2\sqrt 2 } \over 3}} \right),$$ then a value of k is :

A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is :