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 :

The magnitude of the projection of the vector $$\mathop {2i}\limits^ \wedge + \mathop {3j}\limits^ \wedge + \mathop k\limits^ \wedge $$ on the vector perpendicular to the plane containing the vectors $$\mathop {i}\limits^ \wedge + \mathop {j}\limits^ \wedge + \mathop k\limits^ \wedge $$ and $$\mathop {i}\limits^ \wedge + \mathop {2j}\limits^ \wedge + \mathop {3k}\limits^ \wedge $$ , is :

The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1, 1, 0) 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 :