The values of a, for which the points $$A, B, C$$ with position vectors $$2\widehat i - \widehat j + \widehat k,\,\,\widehat i - 3\widehat j - 5\widehat k$$ and $$a\widehat i - 3\widehat j + \widehat k$$ respectively are the vertices of a right angled triangle with $$C = {\pi \over 2}$$ are :

The image of the point $$(-1, 3,4)$$ in the plane $$x-2y=0$$ is :

The two lines $$x=ay+b, z=cy+d;$$ and $$x=a'y+b' ,$$ $$z=c'y+d'$$ are perpendicular to each other if :

Suppose a population A has 100 observations 101, 102,........, 200, and another population B has 100 observations 151, 152,......., 250. If V_A and V_B represent the variances of the two populations, respectively, then $${{{V_A}} \over {{V_B}}}$$ is